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
| x | f(x) | |
| 0 | 4 | |
| 1 | 20 | |
| 2 | 100 | |
| -1 | 0.8 | |
| -2 | 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.
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.
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