exponential problem

Question

The count in a bacteria culture was 700 after 15 minutes and 1800 after 30 minutes. Assuming the count grows exponentially,

What was the initial size of the culture?     

Find the doubling period.     

Find the population after 90 minutes.     

When will the population reach 14000. 

Answer 1

To find P₀ use the initial conditions as follows: 700=P₀e^15k and 1800=P₀e^30k let P₀ =700e^-15k and substitute into the second equation to get 1800 = 700e^15k or 18/7 = e^15k solve for k to get k=.063. Now solve for P₀ =700e^-15•.063 giving P₀ =272.2. For doubling period equation becomes 2=e^.063t which gives t= 11 min. After 90 min P=272.2e^90•.063 and P=78947. When population is 14000 let P=14000= 272e^.063t and doing the math gives t=62.6 min.