Exponential Growth

Question

A colony of bacteria grows exponentially. The colony begins with 4 bacteria, but 4 hours after the beginning of the experiment, it has grown to 27 bacteria.

 

1.) Give a formula for the number of bacteria, P as a function of time t.
Show annual growth rate to four decimal places.

 

 

2.)How long does it take for the colony to triple in size?
Show time t to two decimal places. 

 

Answer 1

Hi Chelsea,

 

Start with the general formula for bacteria growth. p(t) = A e^kt

 

Call the start time to (t note and DO NOT NUMBER IT).

 

This makes the formula work like so, p(to) = A e^kto = 4  eq(1)

 

You also have p(to +4) = A e^k(to + 4) = 27  eq(2)  //the to + 4 is for the four hours

 

Now divide eq(1) by eq(2) and solve for k. When you have k you have the formula k = [ln(27/4)]/4