precalculus,exponential growth

Question

The count in a bacteria culture was 400 after 15 minutes and 1700 after 30 minutes. Assuming the count grows exponentially,

What was the initial size of the culture?    bacteria

Find the doubling period.    minutes

Find the population after 80 minutes.    bacteria

When will the population reach 10000.    minutes

Answer 1

N = Pe^rt, where P = initial amount and N = population at time t

400 = Pe^15r and 1700 = Pe^30r

1700 = P(e^15r)² = P(400/P)² = 160000/P

1700P = 160000

So, P = 94

400 = 94e^15r

4.2553 = e^15r

So, r = 0.09654

N = 94e^0.09654t

Doubling time: Solve for t if 2(94) = 94e^0.09654t

Population in 80 minutes = 94e^0.09654(80)

When is the population 10000: Solve for t: 10000 = 94e^0.09654t