Exponential Function:
Activity: Bacterial population
A population of bacterium in laboratory conditions grows every 20 minutes in 10% the number of specimens. At the beginning of the observation, at 8:00 AM, the population had approximately 3,000,000 individuals:
1. Complete the following attached table (table below) as requested by completing each of the blank boxes.
2. What is the approximate population of bacterium at 10:00 AM?
3. Write the function in power form, indicating which is the dependent and independent variable.
4. Using the function found, determine the bacterial population five hours after the start of the observation.
Answers
Answer:
See below
Step-by-step explanation:
GivenInitial population at 8:00 AM3000000Growth rate = 10% = 1.1 times per 20 minSolution1. Table
Note. I am not sure what are the last 3 rows. Just added next 3 terms.
8:00 ≡ G(0) ≡ 3000000 ≡ 30000008:20 ≡ G(1) ≡ 3000000 *1.1 ≡ 33000008:40 ≡ G(2) ≡ 3000000 *1.1^2 ≡ 36300009:00 ≡ G(3) ≡ 3000000 *1.1^3 ≡ 39930009:20 ≡ G(4) ≡ 3000000 *1.1^4 ≡ 43923002. Population at 10:00
Time passed since 8:00 is 2 hours = 2*3*20 min = 6* 20 minPopulation = 3000000*1.1^6 = 53146833. Function to reflect the population growth
G(x) = 3000000*1.1^xG(x) - is dependent variable, population of bacteriax - is independent variable, time increment of 20 min4. Population after 5 hours
5 hours = 5*3*20 min = 15*20 minG(15) = 3000000*1.1^15 ≈ 12531745Related Questions
Stonebridge neighborhood garage sale have the cash receipts for 5 days:
$136.97
$256.21
$366.10
$176.04
$72.49
Answers
Answer:
$1,007.81
Step-by-step explanation:
Find the distance between the two points rounding to the nearest tenth (if necessary).
(-2,-2) and (0,7).
Answers
Answer:
[tex]d = 9.2[/tex]
Step-by-step explanation:
Given
Points: (-2,-2) and (0,7)
Required
Determine the distance between them.
Distance is calculated as thus:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Where:
[tex](x_1,y_1) = (-2,-2)[/tex]
[tex](x_2,y_2) = (0,7)[/tex]
So, we have:
[tex]d = \sqrt{(0 - (-2))^2 + (7 - (-2))^2}[/tex]
[tex]d = \sqrt{(0 +2)^2 + (7 +2)^2}[/tex]
[tex]d = \sqrt{2^2 + 9^2}[/tex]
[tex]d = \sqrt{4 + 81}[/tex]
[tex]d = \sqrt{85}[/tex]
[tex]d = 9.2[/tex] --- Approximated
Michael has 20 table tennis balls and 16 table tennis paddles. He wants to sell packages of balls and paddles bundled together. What is the greatest number of packages she can sell with no leftover balls or paddles?
Answers
what is the area of the arrow shown?
Answers
what arrow i do not see any picture
Answer:
80 in
Step-by-step explanation:
In the diagram, $AB,$ $BC,$ $CD,$ $DE,$ $EF,$ $FG,$ $GH,$ and $HK$ all have length $4,$ and all angles are right angles, with the exception of the angles at $D$ and $F.$
If perpendicular $EM$ is drawn from $E$ to $DF$ (a close-up is shown below), and if $x$ is the length of $EM,$ then what is $x^2$?
Please help with hints! - no solutions -
If u give a full solution I will report u :P
Also, trolls just wanting to get the 50 points will be reported!
Thanks for the help in advance :)
Answers
Hint: There are some right angles here. What do right angles do in triangles?
Answer:
8
Step-by-step explanation:
Please see the attachment down below.
Hope this helped! :)
Solve.
(12b^2 - 5)(4b^2 + 4)
Answers
Use FOIL
A circular race track has a diameter of 120 ft.about how long would one lap of the track be
Answers
Answer:
The length of one lap of the track would be about 377 feet
Step-by-step explanation:
The length of any circular path is equal to the circumference of the circular pathThe circumference of a circle C = π d, where d is the lengths of its diameter∵ A circular race track has a diameter of 120 feet
→ That means the length of each lap equal the circumference of the track
∴ The length of one lap = C
∵ The diameter of the track is 120 feet
∴ d = 120 feet
∵ C = πd
∴ C = π(120)
→ Use π = 3.141
∴ C = (3.141)(120)
∴ C = 376.92 feet
→ Round it to the nearest whole number
∴ C ≅ 377 feet
∴ The length of one lap of the track would be about 377 feet
Do you think it is true that any solution point to the equation y=1/2x+1 is a point on the line? Explain.
Answers
It is true..
I don't have an explanation.
The volume V of a pyramid is given by the formula V = Bh where B is the area of the base and h is the height
v = 216 cm
B - 36 cm
a. Solve the formula for h
b. Find the height of the pyramid
The height is
centimeters
Answers
Answer:
A. V/B=H B. The height, h, is 6 cm.
Step-by-step explanation:
A. Rearrange the formula V=Bh by dividing both sides by B to isolate h.
B. Plug in the Volume and Base into your rearranged formula to find the height. 216/36= h. h=6
a. The formula for height is h = V/B.
b. The height of the pyramid is 6 centimetres.
What is the total surface area of a given pyramid ?The total surface area of a pyramid is the surface area of the triangular sides in addition to the surface area of the triangular base.
According to the given question we have the volume of the pyramid which is 216 cm³ and base is also given which is 36 cm.
Given V = Bh
∴ h = V/B.
h = 216/36
h = 6 cm.
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plese help im in 2nd grade and this is really hard all the kids in my class know it but me
Answers
Answer:
This isn't in second gradee- x-x
Step-by-step explanation:
Answer: For x such that 0<x<(pie/2), the expression:
[square-root(1-cos^2(x)]/sinx + [square-root(1-sin^2(x)]/cos(x)
is equivalent to,
F. 0
G. 1
H. 2
J. -tan(x)
K. sin2x
The answer is H.
Step-by-step explanation:
Leah borrows £10,000 over 5 years at a simple interest rate of 15%.
Calculate how much interest she will pay over the 5 years?
How much will Leah have to pay back in total
Answers
Answer:
She will pay $7,500 interest over the 5 years
She will have to pay back $17,500 in total
Step-by-step explanation:
Let us revise the rule of the simple interest
I = Prt and A = P(1 + rt) , where:
A = Total Accrued Amount (principal + interest) P = Principal Amount I = Interest Amount r = Rate of Interest per year in decimalt = Time Period involved in months or years∵ Leah borrows £10,000 over 5 years at a simple interest rate of 15%.
∴ P = 10,000
∴ t = 5
∴ r = 15% = [tex]\frac{15}{100}[/tex] = 0.15
→ Substitute them in the first rule to find the interest
∵ I = 10,000(0.15)(5)
∴ I = 7,500
∴ She will pay $7,500 interest over the 5 years
→ Let us find A
∵ A = 10,000(1 + 0.15×5)
∴ A = 17,500
∴ She will have to pay back $17,500 in total
Explain what this student is doing to go from x^2−6x−3= 0 to (x−3)^2 =12
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The student is solving the quadratic equation by completing the square.
Find two consecutive whole numbers that 63 lies between.
Answers
Answer:
They are 62 and 64.
HELPPP PLEASE!!!!! SHOW ALL WORK!!!
Answers
Answer:
22
Step-by-step explanation:
2x+12=x+34
2x-x=34-12
x=22
Casey has 8 1/2 yards of fabric she uses 2 1/2 yards to make pillows and 3 yards to make curtains how much fabric is remaining
Answers
Answer:
3 yards
Step-by-step explanation:
8 1/2 - 2 1/2 = 6
6 - 3 = 3
Your answer is 3.
Please mark as brainliest.
f(x) = x^3 translate 3 units left translate 1 unit down
Answers
Answer:
the function would look like: f(x)=(x³+3)-1
the graph would literally look like the cubic parent graph, just shifted 3 left and 1 down
Which of the binomials below is a factor of this trinomial?
x² + 14x + 40
O AX-9
O B. 32 + 10
O C. X* 14
D. X+4.
Answers
Answer:
D. x + 4Step-by-step explanation:
Let's factor the trinomial:
x² + 14x + 40 = x² + 4x + 10x + 40 = x(x + 4) + 10(x + 4) = (x + 4)(x + 10)x + 4 is between the answer options
Correct option is D.
Use the graph to determine which statement describes f(x).
Answers
Answer:
The statements are not provided, so let's do a complete description of f(x)
In the graph, we can see two asymptotes at x = 1.
This means that the denominator is equal to 0 when x = 1, then we can write:
f(x) = A/(x - 1)
Where we can start thinking that A is a constant.
Now we also can see that when x = 2, f(2) is equal to 1, or:
f(2) = 1.
Then:
f(2) = 1 = A/(2 - 1) = A/1
Then we have A = 1.
Then our function is:
f(x) = 1/(x - 1)
Ten years ago, Lisa bought a hair salon for 182000 dollars. She built up the business and it is now
worth nine times what she paid for it. She decides to sell half of the business to a friend, and they
become partners. Express the amount Lisa's friend must pay Lisa to buy half the business.
Answers
Answer: 819,000
Step-by-step explanation:
182000×9=1638000÷2=819000
Lisa's friend must pay Lisa $819,000 to become her partner in the business, half the worth of Lisa's business today.
What do we mean by the worth of an object?The worth of an object is the price of that object currently. The worth of almost every object in this world is variable (not fixed) with time and use.
How do we solve the given question?In the question, we are said that ten years ago, Lisa bought a hair salon for $182,000. Her business is now worth nine times what she paid.
∴ Worth of the business 10 years ago = $182,000.
Worth of the business now = 9*$182,000 = $1,638,000
We have been informed that Lisa has decided to sell half of her business to a friend. We are asked to find the amount her friend needs to pay, to become her partner.
As we have been told, she is selling half of her business, her friend will need to pay half of her business' worth at the present date.
∴ Her friend pays the amount = 1/2 * worth of the business now
or, Her friend pays the amount = 1/2 * $1,638,000
or, Her friend pays the amount = $819,000.
∴ Lisa's friend must pay Lisa $819,000 to become her partner in the business, half the worth of Lisa's business today.
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2. Describe the process used to solve an equation with variables on both sides.
Answers
Answer:
After simplifying, the first step in solving an equation with a variable on both sides is to Get The Variable On One Side. This is done by reversing the addition or subtraction of one of the terms with the variable. In other words, we must add to both sides or subtract from both sides one of the quantities that contains the variable. It is generally easier to add or to subtract the smaller quantity from the larger quantity, so we are working with positive coefficients, but either way works
1. What are the opposite and absolute value of: a) 7.2 ____,____ b) -3.5 ____, ____ c) 5 ½ ____,____
Answers
Opposite value would be either changing from a positive to a negative or from a negative to a positive.
Absolute value is always a positive value
A) 7.2, -7.2, 7.2
B) -3.5, 3.5, 3.5
C) 5 1/2, -5 1/2, 5 1/2
Answer:
-7.2 7.2
3.5 3.5
-5 1/2 5 1/2
Step-by-step explanation:
WILL GIVE BRAINLIEST!! What are the slope and the y-intercept of the linear function that is represented by the graph?
On a coordinate plane, a line goes through points (0, 3) and (4, 0).
a
The slope is Negative four-thirds, and the y-intercept is 4.
b
The slope is Negative four-thirds, and the y-intercept is 3.
c
The slope is Negative three-fourths, and the y-intercept is 4.
d
The slope is Negative three-fourths, and the y-intercept is 3.
Answers
Answer:
its d
Step-by-step explanation:
y=-3/4+3 I think that's right
Answer:
D- i think because it wouldn't be 4/3 because you cant go over 4 and up three and the y-intrecept is 3
Please vote brainliest :)
A rectangular table is four times as long as it is wide. If the area is 36 ft2, find the length and the width of the table.
Answers
Answer:
The width is 3 ft
The length is 12 ft
Step-by-step explanation:
Let w = width
l = 4w
A = l*w
Replace length with 4w
A = 4w*w
36 = 4 w^2
Divide each side by 4
36/4 = 4w^2/4
9 = w^2
Take the square root of each side
sqrt(9) = sqrt(w)
3 =w
The width is 3 ft
The length is 4*3 = 12 ft
what value of x will make the given triangles congruent?
Answers
Answer:
2
Step-by-step explanation:
Answer:
x = 10
Step-by-step explanation:
The hypotenuse of each of the triangles have to be equal
7x -5 = 4x+25
Subtract 4x from each side
7x -4x-5 = 4x+25-4x
3x -5 = 25
Add 5 to each side
3x-5+5 = 25+5
3x= 30
Divide by 3
3x/3 = 30/3
x = 10
10c - cd + d (if c= -6 and d = 2)
Answers
Answer:
74
Step-by-step explanation:
Substitute the values of the variables into the equation. Good luck on your math journey!
An app developer projects that he will earn $20.00 for every 8 apps downloaded. Write
an equation to represent the proportional relationship between the number of apps and the total earnings
Answers
y = 2.5x
I hope this helps
The required equation is y=2.5x.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
Given that,
Earning of app developer for 8 apps = $20.00
Earning of app developer for 1 app = $2.5
Earning of app developer for x app = $2.5x
Assume, earning of app developer for x app is y
So the equation,
Earning of app developer y=2.5x
The required equation is y=2.5x.
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Someone plz help me
Answers
Answer:
The first order.
Step-by-step explanation:
What do these symbols mean?
The funny shaped line is a square root, meaning what times itself (so for example, 3 x 3) gets that number. So the square root of 9=3.
The small 2 in the top right of the big numbers means square. The opposite. This means multiply that big number by itself twice. If the small number was say, 7, you would multiply the big number by itself 7 times. A common mistake is propel multiply the big number by the small number. The square used in these is 2 to the power of 3, the small number. This means you do 2x2x2, as the small 3 determines how many time you multiply the big number, 2. The result of 2x2x2=8.
The fraction is 11/9. The 9 means how many parts are in a whole number. The 11 means how many of those parts you actually have. Like a pizza-if you had a pizza (the whole) split into 7 parts, 7 would be your bottom number (as the 9 is here). If you are 4 parts and were left with 3 parts, 3 would be your top number (as the 11 is here). Seeing as 11 is bigger than 9, you have to imagine 2 pizzas. Each is split into 9, and you have 11 parts altogether. Thsi is 1 whole pizza and 2 extra parts, making the fraction 1 and 2/9. This is jaut another way to write 11/9 but I find it easier to look at.
The answer?
So. We have established that 11/9 = 1 & 2/9
And that 2 cubed (with the small 3 on it) = 8.
Amd the square roots of 5, 11 and 20 are approximately (Not exactly, but close enough) the following:
5. 2.2
11. 3.3
20. 4.4
So this leaves us a bunch of numbers to put in order from smallest to largest. This is fairly easy. It's not the second one. 8>3.3. It's not the third one. 8>2.2. It's not the fourth one. 1 & 2/9 may be smaller than 8, but 2.2 isn't. So this leaves the first order.
*Note that the symbol > means greater than or bigger than. So 8>2 means 8,is bigger than 2.
Select the correct answer.
Which statement is true about the y-intercept of a quadratic function?
ОА.
A quadratic function can only have one y-intercept.
OB.
A quadratic function can have up to two y-intercepts.
O c.
The y-intercept is also called a zero of the function.
OD
The y-intercept is located at the point where the value of y is 0.
Answers
Step-by-step explanation:
this is the answer .it is right or not
Divide:
−54 ÷ −9 =
pls help llllllllllllllll
Answers
Answer:
Step-by-step explanation:
When you divide two negative numbers, the negative sign cancels. So you just get an answer of 6.
Answer:
6
Step-by-step explanation:
-54 / -9
ok so first of all we can just change them to positive
54 / 9
this is what goes on in my head
the 2 digits equal 9
a number times 9 is just that number less then that number times 10
54 / 9 = 6
-54 / -9 = 6
Put is in order least to greatest. -13/6, -2.1, -26/13, -9/4
Answers
Answer:
-9/4, -13/6,-2.1,-26/13
Answer:
-26/13, -13/6, -2.1, -9/4
Step-by-step explanation:
Sorry its from greatest to least
