Precalculus one math

Question

The count in a bacteria culture was 100 after 20 minutes and 1500 after 35 minutes. Assuming the count grows exponentially,

What was the initial size of the culture?    

Find the doubling period.    

Find the population after 105 minutes.    

When will the population reach 12000. 

Answer 1

This is a pain to do.

A is ending amount

I is the initial amount

base is 2

exponent is a fraction time divided by period of doubling

A = I (2)^(t/ p)

100 = I(2)^(20/ p). 1500 = I(2)^(35\ p)

Take the log of everything

log(100) = log( I) + (20/ p) log(2) do the same for the other equation, then solve each for log( I).

Set the two equations equal to each other and solve for p. I came up with p = 3.839370372 and

I = 2.703200887

I is very close to e^(1), it might work better to use natural log or on. Good luck