Question

I need help setting up the problem...

The number of bacteria in a culture is modeled by the function n(t)=80e^(0.3t) where t is measured in hours. When will the number of bacteria reach 3500? Round your answer to the nearest hundredth of an hour.

a) 53.65 hours
b) 12.59 hours
c) 5.47 hours
d) 3.78 hours
e) 13.38 hours

Answer 1

\[
3500=80e^{0.3t}
\]Solve for \(t\)

Answer 2

hmm?

Answer 3

Okay I understand that and then don't you convert e to ln? I don't understand how to covert it to ln.

Answer 4

Well, we sort of do order of operations backwards.

Answer 5

So the last operation - multiplication - is sorted out first by divided both sides by \(80\).

Answer 6

\[
\frac{175}{4}=e^{0.3t}
\]

Answer 7

Then we can do the natural log. \[
\ln\left(\frac{175}{4}\right) = 0.3t
\]

Answer 8

Oh okay! So then it would be ln(0.3)t?

Answer 9

Final answer\[
\frac{\ln\left(\frac{175}{4}\right)}{0.3} = t
\]

Answer 10

oops too late of a post!

Answer 11

answer 12.59 hours?

Answer 12

\[
\ln e^{\color{red}x} = \color{red}x \\
\ln e^{\color{red}{f(x)}} = \color{red}{f(x)} \\
\ln e^{\color{red}{0.3t}} = \color{red}{0.3t} \\
\]

Answer 13

http://www.wolframalpha.com/input/?i=%5Cfrac%7B%5Cln%5Cleft%28%5Cfrac%7B175%7D%7B4%7D%5Cright%29%7D%7B0.3%7D+%3D+t

I am not a calculator.

Answer 14

Thank you for helping me!