pre calc question

Question

The count in a bacteria culture was 700 after 10 minutes and 1700 after 35 minutes. Assuming the count grows exponentially,

What was the initial size of the culture?    

Find the doubling period.    

Find the population after 120 minutes.    

When will the population reach 10000.   

Answer 1

Use A=Pe^rt

a) Initial size

1700=Pe^35r

700 = Pe^10r

Dividing

1700/700=e^25r

r = ln(1700/700)/25 ≈ 0.0355

P = 700e^-0.355 ≈ 491 bacteria

b) Doulbed

2 = e^0.0355t

t = ln(2)/0.0355 = 19.525 minutes

c) After 120 minutes

491e^0.0355(120) ≈ 34768 bacteria

d) When A=10000

10000 = 491e^rt

t= ln(10000/491)/0.0355 ≈ 84.9 minutes