Question

A population of bacteria is growing according to the function below, where t is in hours. How many hours will it take for the population to grow to 1,000,000 bacteria?
B(t) = 0.5 e^1.5t

Answer 1

Well first we set up this equation like this:

1000000=0.5e^(1.5t)

Answer 2

now we have to solve for t

Answer 3

I was able to get that far, but forgot where to go after that! Help?

Answer 4

Now, what you want to do is divide both sides by 0.5

Answer 5

OK - I get
2,000,000= e^1.5t
now what?

Answer 6

2000000=e^1.5t

Answer 7

now, here is the trick we need to take the natural log of both sides

Answer 8

remind me of that one please, is that e?

Answer 9

lne^1.5t=ln(2000000)

Answer 10

now , the ln and the e will cancel out, since they are inverses of each other, and you well get:

1.5t=ln(2000000)

Answer 11

Now, simply divide both sides by 1/5 to isolate t:

t=1n(2000000)/1.5

Answer 12

OK so when I do that I get
9.672438492
How close am I?

Answer 13

that is the answer, nice job.

Answer 14

THANK YOU!!!!!!