The population P of a culture bacteria is described by P=1609e^.052(t) where t is time in hours.

What was the population at t=6 hours?

1600e ^.052(6)
= 10,112.4971?

Question

The population P of a culture bacteria is described by P=1609e^.052(t) where t is time in hours. 

What was the population at t=6 hours?

1600e ^.052(6)
= 10,112.4971?

anonymous · Answer

Just to be clear, is your equation
$$P=1609e ^{0.052t}$$
or
$$P=1609e ^{0.052}t$$
?

For the first one you get 2198.14
the second one is 10169.29

anonymous · Answer

It's the first one. How did tou come up with that answer?

anonymous · Answer

Plug in t=6. You evaluate the e^(0.052 x 6) and then multiply it by 1609.

anonymous · Answer

Ty, next part, after how many hours will the population reach 8000. Round to the nearest tenth of an hour

anonymous · Answer

$$\large 1600e ^{.052t}=8000$$ solve for $t$

anonymous · Answer

divide by $1600$ and get $$\large e^{.052t}=5$$ and so 
$$\large .052t=\ln(5)$$

anonymous · Answer

Thank you!!! Appreciate the help!