A substance with a half life is decaying exponentially. If there are initially 12grams of the substance and after 70 minutes there are 7 grams, after how many minutes will there be 2 grams remaining?

Answers

Answer 1

Answer:

Step-by-step explanation:

Use the half life formula

[tex]N=N_0e^{kt}[/tex] where N is the amount after decay, No is the initial amount, e is Euler's number, k is the decay constant, and t is the time in minutes. For us, the first equation looks like this:

[tex]7=12e^{k(70)}[/tex] and we will solve that for k and then use that value of k in the second equation to find time.

Begin by dividing 7 by 12 to get

[tex]\frac{7}{12}=e^{k(70)}[/tex] Now take the natural log of both sides since the natural log and that e are inverses. The e then disappears:

[tex]ln(\frac{7}{12})=k(70)[/tex]

Plug the left side into your calculator and then set it equal to the right side, giving us:

[tex]-.5389965007=70k[/tex]

Divide both sides by 70 to get the k value of

k = -.00769995

Now the second equation looks like this:

[tex]2=12e^{(-.00769995)t[/tex] where t is our only unknown now that we know k.

Begin by dividing both sides by 12 to get

[tex]\frac{1}{6}=e^{-.00769995t[/tex] and take the natural log of both sides again to eliminate the e:

[tex]ln(\frac{1}{6})=-.00769995t[/tex]

Take care of the left side on your calculator to get

-1.791759469 = -.00769995t and divide both sides by -.00769995 to get

t = 232.697 minutes


Related Questions

7th grade math help me pleaseee

Answers

Answer:

Number 3

Step-by-step explanation:

In communitive property you can flip the numbers and you will still get the same answer.

Answer:

Associative Property of Multiplication

Step-by-step explanation:

The expression -10 x 3 will equal -30 no matter the order the numbers come in. It can be either -10 x 3 or 3 x -10. This is an example of the associative property of multiplication.

What is -(3x - 12) = 9 x -4

Answers

Answer:

X = 1.3

Step-by-step explanation:

What is the solution for the system of equations that has a sum of 1 and
differece of 9?

Answers

Answer 9

Step-by-step explanation:

What strategies do you use to make a ratio table?

Answers

By multiplying or dividing both quantities in the ratio by the same value to find an equivalent ratio

PLEASE HELLLP I DON"T UNDERSTAND IT!!

Answers

For the first one you mark your first point at 0 and count up 2 and go to the right 3 and mark ur next point and again count up 2 and go to the right 3 times. And then go back to 0 and count down 2 and go to the left 3 times and repeat. For the second one it’s the same thing, mark ur first point at 0, and since the slope is negative you count up 2 and go to the left 1 time and mark ur next point and repeat. To complete the bottom you go back to 0 and count down 2 and go to the right 1 time and repeat. Hopefully this helps!

a room contains 156.1m of air . if the room is 8.31m long and 5.72m wide . use tabe to calculate it height​

Answers

Answer:

height=3.28m

Step-by-step explanation:

air means volume of room

let the height of room be x.

so, volume of room= 156.1 m³

          8.31*5.72*x=156.1m³

           x =3.28m

If zeina has seven times as many books as ali if zeina gave ali 15 books they would eash have the same number of books how many books did each have

Answers

Answer:

Zeina had 35 books and Ali had 5 books

Step-by-step explanation:

Equations

We know Zeina has seven times as many books as Ali. If we call

x = Number of books Ali has

Then Zeina has

7x = Number of books Zeina has

We also know if Zeina gave Ali 15 books, they would have the same number of books, thus:

x + 15 = 7x - 15

Adding 15:

x + 15 +15 = 7x

Subtracting x:

15 +15 = 7x - x

Operating:

30 = 6x

Dividing by 6:

x = 30 / 6

x =5

7x = 35

Thus Zeina had 35 books and Ali had 5 books

What is the value of n in the equation ?

n = 6
n, = 6

n = 0
n, = 0

n = 4
n, = 4

n = 2
n, = 2

Answers

Answer:n = 6

n, = 6

n = 0

n, = 0

n = 4

n, = 4

n = 2

n, = 2

Step-by-step explanation:n = 6

n, = 6

n = 0

n, = 0

n = 4

n, = 4

n = 2

n, = 2 equal to yz7 (*970

Answer:

D.) n=6

Step-by-step explanation:

DOOOOOOOOOOOOOOOOOOOOOGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGYYYYYYYYYYYYYYYYYYYYYYY

Answers

Answer:

woof

Step-by-step explanation:

A pipe is 24 feet long. It needs to be cut into pieces that are each 3/4 feet long. How many pieces can be made from the pipe?

Answers

Hi hi I am going to call you tomorrow and I will call you tomorrow morning I know you’re doing good
36 if you 24 divided by 3/4

In the number 37,278, how many times greater is the 7 in the thousand place

Answers

Answer:

100

Step-by-step explanation:

7000 to 70

7000/70 = 100

Which shows two possible values for a number represented by the point?
0
1
7 and 3
AN
27 and 1
2
2 and 2
O 2 and 2

Answers

27 and 1 is the answer for your question

Answer:

b

Step-by-step explanation:

Select whether the function is discrete or continuous.

Function: The number of basketballs manufactured per day

Answers

Answer:

Continuous

Step-by-step explanation:

Kennedy has 8 feet of ribbon. She wants to cut the ribbon into smaller pieces to make bows, but first she needs to figure out how many inches of ribbon she has. Kennedy knows 12 inches = 1 foot. How many inches of ribbon does she have?

Answers

Answer:

She has 96 inches of ribbon.

Step-by-step explanation:

12 times 8 = 96.

Answer:

so 12 inches = 1 foot

she has 8 feet so,

let x be the amount of ribbon she has

12*8=x

Step-by-step explanation:

12*8=96

she has 96 inches of ribbon

Which statement describes the congruent triangles?
∆WXZ=∆YZX
∆WXZ=∆YXZ
∆WXZ=∆XYZ
∆WXZ=∆ZYX​

Answers

Answer:

A) WXZ=YZX

Step-by-step explanation:

WXZ=YZK

Please help me, thank you!

Answers

Answer:

10*g-4

Step-by-step explanation:

By the way * is multiplicaton

Drag each number to the correct location on the table. Not all numbers will be used.
Jacob performed an experiment with a weighted die, numbered 1 to 6. He rolled the die 125 times and recorded the results. Complete the table below.

24
22
0.176
18
0.232
37
0.048
0.104

Answers

Answer:

Complete Table:

Result of Roll ------ Frequency ------- Experimental Probability

1 --------------------------- 22 ------------------- 0.176

2 --------------------------- 13 ------------------- 0.104

3 --------------------------- 18 ------------------- 0.144

4 --------------------------- 29 ------------------- 0.232

5 --------------------------- 37 ------------------- 0.296

6 --------------------------- 6 ------------------- 0.048

Step-by-step explanation:

Required: Complete the table

The table is divided into 3:

1. Result of Roll

2. Frequency (F)

3. Experimental Probability (P)

The relationship between (2) and (3) is:

[tex]P = \frac{F}{N}[/tex]

Where

N = Number of Rolls

N = 125

For Roll of Result = 2

Frequency = 13

The probability is calculated as thus:

[tex]P = \frac{13}{125}[/tex]

[tex]P = 0.104[/tex]

For Roll of Result = 3

Probability = 0.144

The Frequency is calculated as thus:

[tex]0.144 = \frac{F}{125}[/tex]

[tex]F = 0.144 * 125[/tex]

[tex]F = 18[/tex]

For Roll of Result = 4

Frequency = 29

The probability is calculated as thus:

[tex]P = \frac{29}{125}[/tex]

[tex]P = 0.232[/tex]

For Roll of Result = 5

Probability = 0.296

The Frequency is calculated as thus:

[tex]0.296 = \frac{F}{125}[/tex]

[tex]F = 0.296* 125[/tex]

[tex]F = 37[/tex]

For Roll of Result = 6

Frequency = 6

The probability is calculated as thus:

[tex]P = \frac{6}{125}[/tex]

[tex]P = 0.048[/tex]

For Roll of Result = 1.

To get the frequency; we subtract the sum of frequencies of roll of results 2 to 6 from the total number of rolls.

In other words:

Frequency of 1 = Total Rolls - (Frequency of 2 + Frequency of 3 + Frequency of 4 + Frequency of 5 + Frequency of 6)

Frequency of 1 = 125 - (13 + 18 + 29 + 37 +6)

Frequency of 1 = 125 - 103

Frequency of 1 = 22

The probability is calculated as thus:

[tex]P = \frac{F}{N}[/tex]

[tex]P = \frac{22}{125}[/tex]

[tex]P = 0.176[/tex]

Given are the functions f(x) = x ^ 2 and g(x) = (x - 2) ^ 2 + 1 How can the graph of g(x) be obtained from the graph of f(x) ?

Answers

Answer:

c because it's the opposite

(4c + 7) + (8c + 8)

(adding and subtracting polynomials)

Answers

Answer:

12c + 15

Step-by-step explanation:

Combine like terms

15 rounded to the nearest hundredth

Answers

Step-by-step explanation:

ummmmmmmm how does that work

Solve the system of equations below by graphing them with a pencil and
paper. Enter your answer as an ordered pair.
y=-x+ 2
y=-2x+6

Answers

Answer:

x=2 y=0

Step-by-step explanation:

Explanation:

just put y= -x in second equation x comes out to be 2. Then put x=2 y comes out to be 0

The straight line L has equation y = 2x - 5
Find an equation of the straight line perpendicular to L which passes through (-2, 3).

Answers

Answer:

slope of perpendicular line - m = -1/2

passing through (-2,3)

thus,

y-3 = -1/2 (x+2)

or y = -1/2x +2

An equation of the straight line perpendicular to [tex]\boldsymbol{y=2x-5}[/tex] which passes through [tex]\boldsymbol{(-2,3)}[/tex] is [tex]\boldsymbol{x+2y-4=0}[/tex]

An equation of a straight line is [tex]\boldsymbol{y=2x-5}[/tex]

Compare this equation with the form [tex]\boldsymbol{y=mx+b}[/tex] where [tex]\boldsymbol{m,b}[/tex] denote slope and [tex]\boldsymbol{y-}[/tex]intercept respectively.

So,

[tex]\boldsymbol{m=2}[/tex]

As the slopes of two perpendicular lines are negative reciprocals of each other, slope of a required line is equal to [tex]n=\frac{-1}{2}[/tex]

Take [tex](x_1,y_1)=(-2,3)[/tex]

Equation of the required line is [tex]\boldsymbol{y-y_1=n(x-x_1)}[/tex]

       [tex]y-3=\frac{-1}{2}(x+2)[/tex]

     [tex]2y-6=-1(x+2)[/tex]

[tex]x+2y-4=0[/tex]

For more information:

https://brainly.com/question/20632687?referrer=searchResults

Is finding the value for the variable the only solution to real-world problems? Explain.

Answers

Answer:

The answer is "No. In many real-world scenarios, the variable is a value that is compared to other quantities. The value for the variable is used to find the quantities it is compared to".

Step-by-step explanation:

how many $10 bills are equal to a $1000 bill?

Answers

100 ten dollar bills are equal to 1000.If you divide 1000 by 10 you get 100.

How many $10 bills are equal to a $1000 bill?$10 × $100 = $1,000 .The answer is a hundred 1 ten five cents.S: 10, 20, 30, 40, 50, 60, 70, 80, 81, 82, 83, 84, 85.The $1,000 banknote is still recognised as legal tender despite having been phased out for more than 50 years. This implies that any $1,000 banknote you come across is worth at least its face value, or $1,000. $10 and $20 bills can be obtained through Citibank, Capital One, Bank of America, Chase, and PNC.1,000 is 10 hundreds.

To learn more about  $10 bills  refer

https://brainly.com/question/1838778

#SPJ2

A simplified model for the concentration (micrograms/milliliter) of a certain slow-reacting antibiotic in the bloodstream t hours after injection into muscle tissue is given by
f(t) = t2 ·e−t/16, t ≥ 0.
When will there be maximum concentration?
In the units given, how much is the maximum concentration?
When will the concentration dip below a level of 20.0?
Estimate from a graph when the concentration function changes concavity

Answers

Answer:

A) T = 24

b) 77.953

c)  t > 63.78 , t < 5.6

d) (7.029,27.5) and (40.97,55.23)

Step-by-step explanation:

Given

F(t) = t^2 e^-t/12, t ≥ 0

a) time for maximum concentration

  t = 24

b) determine maximum concentration at maximum time

F(24) = 77.953

c) determine when the concentration will dip below the level of 20.0

when t > 63.78 , t < 5.6

d) concentration function changes concavity  ( estimated from a graph )

(7.029,27.5) and (40.97,55.23)

attached below is the detailed solution

PLZ HURRY I WILL GIVE BRAINLIEST (50 points)

A person weighs a different amount on other surfaces in space than they do on Earth because the gravitational pull of each surface is different than that of Earth. The table and graph show the weights of objects on Earth, Mars, and the Moon.


Weight on Earth and Mars
Weight on Earth, e
90 pounds
120 pounds
160 pounds
Weight on Mars, a
36 pounds
48 pounds
64 pounds




Weight on Earth and Moon
A graph has weight on earth (pounds) on the x-axis, and weight on moon (pounds) on the y-axis. A line goes through points (60, 10) and (120, 20).


If a person weighs 240 pounds on Earth, what would be the difference in weight of the same person on Mars and on the Moon (based on the table and graph)?
The person weighs 56 pounds more on Mars than on the Moon.
The person weighs 56 pounds more on the Moon than on Mars.
The person weighs 560 pounds more on Mars than on the Moon.
The person weighs 560 pounds more on the Moon than on Mars.

this is on edge2020

Answers

Answer:

The answer is A The person weighs 56 pounds more on Mars than on the Moon.

Step-by-step explanation:

Answer:

the first answer

Step-by-step explanation:

did it on edge

I need help with the three of them with a step by step example please

Answers

Answer:

4

Step-by-step explanation:

Please help me!!! 10 points and I will count u as brainliest

Answers

Answer:

F or H

Step-by-step explanation:

not J because that is negative,  not G because that means none, so either H or F. I'm not going to give you the whole answer but another hint is look at the circles are they circled or non circlircled. I eliminated two answers for you.

remember what your teachers saids: what does it mean for the circlies to be colored or blank.

good luck!

(GIVING BRAINLIEST!!)


Two magnets push away from each other and do not attract. What do we know to be true and what type of force is being demonstrated? Write 2 or more sentences to support your answer :)

Answers

Answer: it could be a mangintic force..  Because if two magnets a.k.a the north and south pole magnets are brought together they will push each other away instead of sticking.

Hope this helps

Answer:

They are repeling because they are both negitively charged

Step-by-step explanation:

please mark brainelist

Find m 8
B
47°
8
O
8
O
47
O
90
O
180

Answers

The answer is B 47.
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