How do I find the exponential key/growth of something?

Question

This is the problem:

 

The number of bacteria in the petri dish quadrupled every hour. There were 1000 bacteria at t=0

a) write an exponential equation that expresses the number of bacteria as a function of time

b) Using the equation in (a) find how many bacteria there were at t=24

 

How do i do a) and b)??

Answer 1

The general form for an exponential growth equation is P(t) = Ae^(rt), where P(t) is the number of bacteria after time t, A is the initial number, and r is the growth rate.

If they quadruple every hour, then P/A = 4 when t = 1.

So 4 = e^(r*1).  Taking LN of both sides gives

r = LN(4) ~= 1.39

a) Substituting back into the original equation with A = 1000 gives

P = 1000*e^(1.39*t)

b) at t = 24, simply substitute 24 in for t:

P = 1000*e^(1.390.6*24) = 2.81e17