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 5,000 bacteria? Round your answer to the nearest integer.
B(t)=20*e^(1.5t)

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 5,000 bacteria? Round your answer to the nearest integer. 
B(t)=20*e^(1.5t)

anonymous · Answer

$$20e^{1.5t}=5000$$ solve for $t$

anonymous · Answer

divide by 20
take the log
divide by 1.5

anonymous · Answer

you got this?

anonymous · Answer

yes i think, give me a min

anonymous · Answer

166.6666666 @satellite73

anonymous · Answer

lets check 
divide by 20 and get 
$$e^{1.5t}=250$$

anonymous · Answer

in equivalent logarithmic form, this is the same as 
$$1.5t=\ln(250)$$

anonymous · Answer

divide by $1.5$ and get 
$$t=\frac{\ln(250)}{1.5}$$ now we need a calculator

anonymous · Answer

http://www.wolframalpha.com/input/?i=ln%28250%29%2F%281.5%29

anonymous · Answer

3.6810

anonymous · Answer

i guess yes

anonymous · Answer

yay :D