Evaluate an exponential function

This lesson will show how to evaluate an exponential function and how to solve a real-world problem by evaluating an exponential function.

Example #1

Evaluate the following function for x  = 0, 1, 2, -1, -2

f(x) = 4 × 5^x

x	4 × 5x	f(x)
0	4 × 50 = 4 × 1 = 4	4
1	4 × 51 = 4 × 5 = 20	20
2	4 × 52 = 4 × 25 = 100	100
-1	4 × 5-1 = 4 × 1/5 = 4/5	0.8
-2	4 × 5-2 = 4 × 1/25 = 4/25	0.16

Evaluate an exponential function to solve a real-world problem.

Example #2

Suppose 30 toads are taken to an island. The toad population quintuple every 3 months. Model this situation with an exponential function and then evaluate the function to find how many toads would there be after 4 years.

Solution

Important keys words to understand this problem are 'quintuple' and 'every 3 months'.

Quintuple:

The word quintuple means that the population was increased 5 times.

Every 3 months:

Every 3 months is the same as every one-fourth of a year or 1 quarter.

Let x be the number of quarters, then f(x) = 30 × 5^x

For this problem, there are 4 quarters in a year since the growth is happening every 3 months. For two years then, we get 8 quarters.

f(8) = 30 × 5⁸

f(8) = 30 × 390625

f(8) = 11718750

After two years, there will 11,718,750 toads in that island.