Bacteria culture starts with 300 bacteria

[justin345]

Homework Statement

and after 3 hours there are 600 bacteria. Assuming bacteria grow at rate proportinal to their size, which means you can use the function, y=Ae^kt, where y is the number of bacteria and t is time in hours.

1) find the number of bacteria after 5 hours,
2) when will the population reach 2,000?

Homework Equations

The Attempt at a Solution

First, find k:
600=300e^3k
2=e^3k
k=1/3*ln(2)=0.231

1) y=300e^5*0.231=952.207
2) 2000=300e^0.231t
6.667=e^0.231t
t=1/0.231 ln (6.667)=8.21


Please check my answers.
J.

 

[HallsofIvy]

Your first answer should not be a fraction- the "number of bacteria" must be an integer. Use 952.

You should always include units. For number 2 your answer should be "8.21 hours".

Other than that, they are correct.