What is an exponential function ?

The general form of the exponential function can be written :
               f(x) = ab^x
a is the initial value and b is the growth rate.

Let's look at this problem :
      The growth of bacteria in a dish is modeled by the function f(t) = 2^ n . For which value of t is f(t) = 32 ?
                                                                                                             3
The first step is to write out the exponential function .
          32 = 2^ t 
                       3
Next find a common base . To do this you can turn 32 into 2^5 because 2 to the fifth power is 32.

The new function becomes : 2^5 = 2^ t 
                                                          3
Now you solve for x : 5 =  t 
                                         3
You do this by multiplying 3 to every side.
You final answer becomes t = 15.


Now Try It Yourself : 
   A population of rabbits double every 60 days according to the formula P=10(2)^ 1 , where P is the population of rabbits on day t. 
                             60
What is the value of t when the population is 320 ?