1. In 2012, the population of a city was 5.68 million. The exponential growth rate was 2.99% per year.
a) Find the exponential growth function.
b) Estimate the population of the city in 2018.
c) When will the population of the city be 10 million?
d) Find the doubling time.
Answers
Answer:
So first we need to determine what the exponential growth function would look like. Exponential growth functions look like [tex]P(t) = P_0*e^{r*t}[/tex] and in our case [tex]P_0[/tex] would be the initial population which is 5.68 million. R is the next variable that we need to fill out which is the rate of change which in our case is 2.99% or 0.0299.
This is how our function should look now [tex]P(t)=5.68*e^{0.0299*t}[/tex]
Moving onto part b, we need to estimate the population of the city in 2018 which 6 years from 2012 and we plug that into t and solve.
[tex]P(t)=5.68*e^{0.0299*6}[/tex]
[tex]P(t)=5.68*e^{0.1794}[/tex]
[tex]P(t) = 5.68*1.1965[/tex]
[tex]P(t) = 6.796\ million[/tex]
Moving onto part c, we need to find when the population of the city will be 11 million which will be done by setting P(t) to 10 million and solving for t.
[tex]10 = 5.68*e^{0.0299*t}[/tex]
[tex]\frac{10}{5.68} = \frac{5.68*e^{0.0299*t}}{5.68}[/tex]
[tex]1.76056=e^{0.0299*t}[/tex]
[tex]ln(1.76056)=ln(e^{0.0299*t})[/tex]
[tex]\frac{0.5656}{0.0299}=\frac{0.0299*t}{0.0299}[/tex]
[tex]18.9175\ years = t[/tex]
Moving onto part d, we need to find the doubling time. This will be similar to the previous part but we will be finding the time it takes to double our population. So instead of putting 10 million for P(t) we put 5.68* 2 in there which is 11.36.
[tex]11.36= 5.68*e^{0.0299*t}[/tex]
[tex]\frac{11.36}{5.68} = \frac{5.68*e^{0.0299*t}}{5.68}[/tex]
[tex]2=e^{0.0299*t}[/tex]
[tex]ln(2)=ln(e^{0.0299*t})[/tex]
[tex]\frac{0.693}{0.0299}=\frac{0.0299*t}{0.0299}[/tex]
[tex]23.182\ years = t[/tex]
Hope this helps! Let me know if you have any questions
Related Questions
Please explain how to get the answer too! I'm so confused.
Answers
Answer:
360
Step-by-step explanation:
So I did 5 x 6 x 6 x 2 = 360
Srekar needs to increase the length, width, and height of the prism below by 2 inches. The original prism has a length of 3 inches, a width of 2 inches, and a height of 1 inch.
A prism has a length of 3, height of 1, and width of 2.
Which statements about the new prism are true? Select three correct answers.
The new prism will have a length of 5 because 3 + 2 = 5.
The new prism will have a width of 4 because 2 + 2 = 4.
The new prism will have a height of 2 because 1 times 2 = 2.
The volume will increase by 6 because 2 times 3 = 6 and each of the 3 dimensions is increased by 2.
Srekar could increase the volume by the same amount by just adding 6 to the height instead of 2 to each side.
The volume of the new prism will be 20 times 3 = 60 because there will be 20 cubes in each layer and the height will be 3 so there will be 3 layers of 20 cubes each.
Answers
The three correct statements are:-
The new prism will have a length of 5 because 3 + 2 = 5.The new prism will have a width of 4 because 2 + 2 = 4.The new prism will have a height of 2 because of 1 time 2 = 2.What is a rectangular prism?
A rectangular prism is a three-dimensional rectangular object having all surfaces rectangular.
It is given in the question:-
Sarkar needs to increase the length, width, and height of the prism below by 2 inches. The original prism has a length of 3 inches, a width of 2 inches, and a height of 1 inch. A prism has a length of 3, a height of 1, and a width of 2.
The solution will be:-
The new prism will have a length of 5 because 3 + 2 = 5.The new prism will have a width of 4 because 2 + 2 = 4.The new prism will have a height of 2 because of 1 time 2 = 2.
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HELP ASAP- NO LINKS AND NO JOKES
a student solved a system of equations as shown below
3x+2y=7
5x-4y=-3
which step in the solution contains the first error
A. Step 4
B. Step 6
C. step 2
D. Step 1
Answers
Answer:
A
Step-by-step explanation:
step 3 is correct
x = 1
in step 4 the student has substituted x = 1 into y instead of x, that is
3x + 2(1) = 7 ← Incorrect substitution
Should be
3(1) + 2y = 7
3 + 2y = 7 ( subtract 3 from both sides )
2y = 4 ( divide both sides by 2 )
y = 2
Answer:
A. Step 4
Step-by-step explanation:
Identifying the error
In step 4 the value of x is supposed to be substituted into the second equation however the value of x is instead substituted for y which is the first error made
Solving it correctly and explaining each step.
We have the two equations 3x + 2y = 7 and 5x - 4y = -3
It appears that the elimination method is being used as the first step consist of multiplying the first equation by 2 so that we have the two variables -4y and 4y which can cancel out in the next step so we are going to use the elimination method as well to solve it correctly.
What is the elimination method?
The elimination method is a method used to solve a system of equations. When you have two variables that have the same coefficient ( number before variable; x or y ) but different signs ( it works if they have the same too ) you can add the two equations eliminating one of the variables. Using this method will leave you with a singular variable in which you can solve
Solving it using the elimination method
Again we have the two equations 3x + 2y = 7 and 5x - 4y = -3
(step 1) Notice how the first equation has 2y which can be multiplied by 2 resulting in us getting 4y which is opposite of -4y. This sets us up exactly for using the elimination method.
Thus the first step would be too multiply the first equation by 2
3x + 2y = 7
x2
------------------
6x + 4y = 14
Now we have the two equations 6x + 4y = 14 and 5x - 4y = -3
(step 2)Our next step would be to add the two equations so that the variable y is eliminated
6x + 4y = 14
+ 5x - 4y = -3
--------------------
11x 0 = 11
We're left with 11x = 11
(step 3)Our next step would be to solve for x
11x = 11
==> divide both sides by 11
x = 1
(step 4) Now that we have defined one of are variables we plug it in into one of the equations and solve for the other, this is step 4.
5x - 4y = -3
==> plug in x = 1
5(1) - 4y = -3
(step 5)==> simplify
5 - 4y = -3
(step 6) ==> subtract 5 from both sides
-4y = -8
(step 7) ==> divide both sides by -4
y = 2
The real solution would be (1,2)
can anyone please solve this and tell me if it's correct please
Answers
Answer:
Q1. 15
Q2. You're correct
Q3. 3.60
Q4. 2 Correct
Step-by-step explanation:
Can you help me please?
Answers
96 / 8 = 12
98 / 9 = 10.88 or 10.9 (rounded)
pls help me
45 points just to help me with this plsss
Answers
Answer:
64 cm²
Step-by-step explanation:
Formula(s):
Surface area = Sum of the area of the prism's facesArea of triangle: 1/2 x Base x HeightArea of square: (side)²Clearly, we can see that there are 4 triangles and a square included in the prism. Therefore,
⇒ Surface area = 4(Area of triangle) + Area of squareWe know the following:
Given height of triangle: 6 cmGiven base of triangle: 4 cmSince the base of the triangle is equivalent to the side of square (As shown in picture), the side of the square must be 4 cm.
⇒ Surface area = 4(1/2 x Base x Height) + (side)²⇒ Surface area = 4(1/2 x 4 x 6) + (4)²⇒ Surface area = 4(12) + 16⇒ Surface area = 48 + 16⇒ Surface area = 64 cm²Therefore, the surface area of the prism is 64 cm².
You randomly draw a marble from a bag of 72 marbles, and then replace the marble. You do this 30 times and record your results in Tally chart. Base on these results, how many marbles in the bag are grey?
Answers
Answer:
2160
Step-by-step explanation:
You just have to mutiply, 72 x 30 is 2160. So the answer is there are still 2160 marbles in the bag that are grey!
Please mark branliest!!!
Answer:
30 ≥ x ≥ 0
Step-by-step explanation:
I don't think this is the full question but if it is the answer above should be right.
Have a nice day! :)
The selling price of an item is $720. It is marked down by 30%, but this sale price is still marked up from the cost of $420. Find the markup from cost to sale price.
Answers
The markup cost is $84 if the selling price of an item is $720. It is marked down by 30%, but this sale price is still marked up from the cost of $420.
What is markup price?Markup pricing is the practice in which the price of products or commodity is determined by taking all the goods together and adds a fraction as a markup.
We have:
The selling price of an item is $720. It is marked down by 30%
[tex]\rm = 720\times \dfrac{30}{100}[/tex]
Markdown = 216
Now subtract it from the selling price:
= 720-216
Sale price = 504
Now,
= 504-420
Markup cost = $84
Thus, the markup cost is $84 if the selling price of an item is $720. It is marked down by 30%, but this sale price is still marked up from the cost of $420.
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can someone help me with this.........asap
Answers
(You have to use the table to answer the question)
Can someone help I don’t understand.
Answers
Answer:
that is reading my friend
Step-by-step explanation:
Answer:
Sidney is shallow but busy. One common boating hazard in this city are the rocks, stingrays, and sharks. Rounf trip fair: $2000 hotel cost: 250 for 1 night and and or 2500 for 10 nights. total travel expense: $4500.
Step-by-step explanation:
Sidney is shallow but busy. One common boating hazard in this city are the rocks, stingrays, and sharks. Rounf trip fair: $2000 hotel cost: 250 for 1 night and and or 2500 for 10 nights. total travel expense: $4500.
Find the area of the rhombus. using 9cm and 6cm
Answers
Answer:
27
Step-by-step explanation:
The formula is pq/2. If you plug in your values, you will get 27.
2.Select all the expressions that are equivalent to 6-X.
Equivalent to 6 - x
a. X- 6
b. 6 + -x
c. -x + 6
d. -6 + x
e. 6 + x
Answers
[tex]\textbf{b.)} ~ 6+(-x)\\\\\textbf{c.)} ~ -x+6\\[/tex]
This cylindrical fish tank has a height of 38 inches and a diameter of 26 inches. What is the volume of the fish tank? Use 3.14 for . Round to the nearest inch.
Answers
The volume of the fish tank having height 38 inches and diameter 26 inches = 20,165.08 [tex]inch^{3}[/tex]
What is Volume of cylinder?The volume of a cylinder is the number of unit cubes (cubes of unit length) that can be fit into it. It is the space occupied by the cylinder as the volume of any three-dimensional shape is the space occupied by it.
The height of the fish tank = 38 inches
Diameter = 26 inches
Radius of fish tank = 13 inches
Volume of the fish tank =[tex]\pi* r^{2}*h[/tex]
= 3.14 x 13 x13 x 38
= 3.14 x 169 x 38
= 20,165.08 [tex]inch^{3}[/tex]
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alg 1 adding/subtracting with rational expression
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's evaluate ~
As the denominator of both the terms is same, we can simply perform subtraction on numerator.
That is :
[tex]\qquad \sf \dashrightarrow \: \dfrac{a - 2}{ {a}^{2} + 7a + 6 } - \dfrac{5a - 6}{ {a}^{2} + 7a + 6 } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{a - 2 - (5a - 6)}{ {a}^{2} + 7a + 6 } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{a - 2 - 5a + 6}{ {a}^{2} + 7a + 6 } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{ - 4a + 4}{ {a}^{2} + 7a + 6 } [/tex]
Answer:
-4a + 4/ a^2 + 7a +6
what is the slope of a line that passes through the points (-3,7) and (7,5)
Answers
Answer:
the answer IS. -1/5 which it could be written as -0.2. NOTE: please consider the negative signs in calculating
HELPP ASAP!! ILL MAKE YOU THE BRAINIEST!
Using the given diagram solve for x
Answers
Answer:
x = 5
Step-by-step explanation:
the angle bisector divides the opposite sides into segments that are proportional to the other 2 sides , that is
[tex]\frac{x}{3}[/tex] = [tex]\frac{10}{6}[/tex] ( cross- multiply )
6x = 30 ( divide both sides by 6 )
x = 5
What does 18x12x1000 equal to?
Answers
Because 1000 has 3 zeros, add 3 zeros after 216. Answer is 216,000
First, we calculate 18 x 12
18 x 12 = 216.
To multiply a number by 1000, we add 3 zeros after it.
So, 216 x 1000 = 216000
-> 18 x 12 x 1000 = 216000.
If data set A has a larger standard deviation than data set B, data set B is
more spread out than data set A.
REST
TE
TER
O A. True
B. False
Answers
Reason:
Data set A has the larger standard deviation, so it is more spread out.
Find the angle x on the line. a triangle has 38 at the top and 101 on the outside of it.
Answers
Answer:
x=79°
Step-by-step explanation:
[tex]x + 101 = 180( < \: on \: str \: line = 180) \\ x = 180 - 101 \\ x = 79[/tex]
Help me answer this please
Answers
Answer:
1. d
2 c
3 a
4 g
5 h
6 e
7 b
8 f
9 i
10 j
Step-by-step explanation:
Ann weighs 259 pounds but is only 5 feet 3 inches tall. Betty is 6 feet tall. How much would you expect Betty to weigh if they have the same height/weight ratio?
A. 226.62 LBS
B. 24 LBS
C. 518.00 LBS
D. 296.00 LBS
I WILL GIVE BRAINLELIST
Answers
Answer:
D. 296.00 LBS
Step-by-step explanation:
We convert both heights to inches.
1 ft = 12 in.
5 ft 3 in = 5 × 12 in. + 3 in. = 63 in.
6 ft = 6 × 12 in. = 72 in.
[tex] \dfrac{63~in.}{259~lb} = \dfrac{72~in.}{x} [/tex]
[tex] \dfrac{63x}{259} = 72~lb [/tex]
[tex] x = \dfrac{259 \times 72~lb}{63} [/tex]
[tex] x = 296~lb [/tex]
Answer: D. 296.00 LBS
x^2 - 3 = 1
Please help me with this I need a answer and explanation so I can do this on my own asap!
Answers
Answer:
x=2
x=-2
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
x^2-3-(1)=0
1.1 Factoring: x2-4
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 4 is the square of 2
Check : x2 is the square of x1
Factorization is : (x + 2) • (x - 2)
Equation at the end of step
1
:
(x + 2) • (x - 2) = 0
STEP
2
:
Theory - Roots of a product
2.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
2.2 Solve : x+2 = 0
Subtract 2 from both sides of the equation :
x = -2
Solving a Single Variable Equation:
2.3 Solve : x-2 = 0
Add 2 to both sides of the equation :
x = 2
180 : 60 simplified pls
Answers
Answer: Heyaa!
60 Cant be Simplified so it stays the same.
Step-by-step explanation:
Nothing further can be done with this topic.
Hopefully this helps you !
- Matthew ~
simplify negative square root of 72
Answers
Explanation: You’ll have to find where the original product can be rooted. 36 & 2. 36 is a perfect square, so it becomes 6.
Then 6 is on the outside, while two is inside.
Don’t forget the negative.
Pls help, will mark brainliest!!
1. Phil is about to take a test that contains matching questions worth 10 points each and essay questions worth 25 points each. He must do at least 3 matching questions, but time restricts doing more than 12. Phil must do at least 4 essays, but time restricts doing more than 15. If no more than 20 questions can be answered, how many of each type should Phil do in order to maximize his score?
a. Define variables and write constraints for this problem.
b. Write an equation for what you want to maximize or minimize.
Answers
Answer:
hope you can understand
Order the cities according to population density (persons/sq. km), from greatest to smallest.
Answers
Answer:
Step-by-step explanation:
City Population Density (Persons/Square Mile) 2016 Population Land A...
New York, New York 28,211 8,537,673 303
Los Angeles, California 8,484 3,976,322 469
Chicago, Illinois 11,883 2,704,958 228
View 751 more rows
find the area of the red shaded region round to the nearest tenth.
Answers
Answer:
28.5 in²
Step-by-step explanation:
find the area of the quarter circle:
(pi x r²)/4
100pi/4 =
25pi
To get the shaded region minus the triangle from the quarter circle:
Formula for triangle is bh/2
25 pi - Area of triangle
25 pi - (10x10)/2
25pi - 50
Which is approximately 28.5 square inches.
If p= -1,-1 find the image p under the following rotation 70 degrees counterclockwise
Answers
I know
Step-by-step explanation:
I wish I it but i dont and i think that other person will
(using tables of x- and y-values).
x² - 3= 2x
a. X= -1 or x = 3
C. X = -3 or x = -3
b. x= 2 or x = -3
d.x=1 or x = -1
I need help with this plss
Answers
Answer:
a
Step-by-step explanation:
x² - 3 = 2x ( subtract 2x from both sides )
x² - 2x - 3 = 0 ← in standard form
consider the factors of the constant term (- 3) which sum to give the coefficient of the x- term (- 2)
the factors are - 3 and + 1 , since
- 3 × + 1 = - 3 and - 3 + 1 = - 2 , then
x² - 2x - 3 = (x - 3)(x + 1) = 0 ← in factored form
equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
x - 3 = 0 ⇒ x = 3
The pythagorean theorem applies to what kind of triangle?.
Answers
Answer:
Right angled triangle
Step-by-step explanation:
Right angled triangle has angle of 90degree
Answer:
Step-by-step explanation:
It applies only to a right angled triangle.
