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.
Notice that this time, we used a table to organize our calculations. It is always good practice to use a table when evaluating exponential functions.
x | f(x) | |
0 | 4 | |
1 | 20 | |
2 | 100 | |
-1 | 0.8 | |
-2 | 0.16 |
Notice that you can also write the answers as shown below:
f(0) = 4
f(1) = 20
f(2) = 100
f(-1) = 0.8
f(-2) = 0.16
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 be there after 4 years.
Solution
There are two Important keys words to understand in this problem and these 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.
Notice that when x = 0, f(0) = 30×5^{0}
f(0) = 30×1
f(0) = 30.
x = 0 refers to the starting point or the day the toads were taken to the island.
May 07, 21 02:29 PM
A time-series data shows information about the same subject or element of a sample or population for different periods of time.
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