The count in a bacteria culture was 200 after 20 minutes and 1500 after 35 minutes Pls help me answer this question

Question

The count in a bacteria culture was 200 after 20 minutes and 1500 after 35 minutes. Assuming the count grows exponentially, What was the initial size of the cultie? Find the doubling period. Find the population after 60 minutes. When will the population reach 10000. You may enter the exact value or round to 2 decimal places.

Answer 1

1) 200 = a₀(e^20k)

2) 1500 = a₀(e^35k)

3) 7.5 = e^15k, divide 2) by 1)

4) ln 7.5 = 15k, solve for k

Use k in formula for 60 minutes and population of 10000