# Thread: exponential growth and decay

1. ## exponential growth and decay

Hi everyone,

Could someone please tell me if this is correct?

A cell divides into two cells every 20 minutes. The initial population of a culture is 60 cells

Find and expression for the number of cells after t hours:

(0,60) (20, 132)

132=600e^k20
ln2.2=lnk^20
ln2.2/20=20k/20
k=ln2.2/20

y(t)=60e^ln2.2/20t

Find the number of cells after 8 hours:

y(8)=60e^ln2.2/20(8)

Find the rate of growth after 8 hours:

Isn't that just -2.2% but it can't be negative. ???????????

When will the population reach 20,000 cells?

20000=60e^-2.207t
t=-2.63 This can't be right. It can't be a negative number, right?

Thank you very much

2. Originally Posted by chocolatelover
Hi everyone,

Could someone please tell me if this is correct?

A cell divides into two cells every 20 minutes. The initial population of a culture is 60 cells

Find and expression for the number of cells after t hours:

(0,60) (20, 132)

132=600e^k20
ln2.2=lnk^20
ln2.2/20=20k/20
k=ln2.2/20

y(t)=60e^ln2.2/20t

Find the number of cells after 8 hours:

y(8)=60e^ln2.2/20(8)

Find the rate of growth after 8 hours:

Isn't that just -2.2% but it can't be negative. ???????????

When will the population reach 20,000 cells?

20000=60e^-2.207t
t=-2.63 This can't be right. It can't be a negative number, right?

Thank you very much
first off, where did you get 132 from? secondly, your formula was designed for t measured in minutes, you can't plug in 8 for t then, you would need to plug in 480. otherwise, make your formula with respect to hours to begin with

3. secondly, your formula was designed for t measured in minutes, you can't plug in 8 for t then, you would need to plug in 480. otherwise, make your formula with respect to hours to begin with
Where did you get 480 from? Can you show me how to set up the formula? If I were to have had the right numbers would that have worked?

Thank you

4. Originally Posted by chocolatelover
Where did you get 480 from? Can you show me how to set up the formula? If I were to have had the right numbers would that have worked?

Thank you
you plugged in t in minutes when you were deriving the formula. so you need to plug in t in minutes when answering your question, 8 hours = 480 minutes. i would have changed 20 minutes to hours first, the numbers are nicer to deal with.

20 minutes = 1/3 hour, so begin by solving $120 = 60e^{r/3}$ for $r$

5. So, r=2.079

y(t)=60e^2.079t

For the next part (find the number of cells after 8 hours) I would just plug in 8 for t, right?

Find the growth rate after 8 hours?

8=60e^2.079t

I would solve for t, right?

Thank you

6. Originally Posted by chocolatelover
So, r=2.079

y(t)=60e^2.079t

For the next part (find the number of cells after 8 hours) I would just plug in 8 for t, right?

Find the growth rate after 8 hours?

8=60e^2.079t

I would solve for t, right?

Thank you
no, t is time, you replace t with 8 and solve for y(t)