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) = 30×50

f(0) = 30×1

f(0) = 30.

x = 0 refers to the starting point or the day the toads were taken to the island.

Jun 09, 23 12:04 PM

Jun 06, 23 07:32 AM

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