Activity
Examine the graph representing an exponential function . The function gives the value of a computer, in dollars, as a function of time, , measured in years since the time of purchase.
Based on the graph, what can you say about the following?
1. The purchase price of the computer
Compare your answer:
$400
2. The value of when is 1
Compare your answer:
3. The meaning of
Compare your answer:
The value of the computer after 1 year
4. How the value of the computer is changing each year
Compare your answer:
The computer loses half of its value each year.
5. An equation that defines . (If needed, use the '^' symbol to enter an exponent.)
Compare your answer:
or equivalent (i.e., ).
6. Whether the value of will reach 0 after 10 years
Compare your answer:
No, it will not. After 10 years, the value of the computer will be a little less than $0.40.
For questions 7 - 10, examine the graphs of the exponential functions.
Examine the graph of the exponential function below.
7. Write an equation that defines the function. Use the “^” symbol to enter an exponent.
Compare your answer:
8. For each, write an equation that defines the function and find the value of the function when is 5.
Compare your answer:
Examine the graph of the exponential function below.
9. Write an equation that defines the function. Use the “^” symbol to enter an exponent.
Compare your answer:
(or equivalent, i.e., ).
10. For each, write an equation that defines the function and find the value of the function when is 5.
Compare your answer:
Video: Interpreting an Exponential Function from a Graph
Watch the following video to learn more about interpreting exponential functions:
Are you ready for more?
Extending Your Thinking
Consider a function defined by .
If the graph of goes through the points and , would you expect to be less than, equal to, or greater than 20?
If the graph of goes through the points and , would you expect to be less than, equal to, or greater than 20?
Compare your answer:
The value 20 is what you would get for if were a linear function through and (or and ). Looking at graphs representing our exponential functions, we can see that the line connecting two points on the graph always seems to be above the graph of the exponential function itself. Thus, we would expect in both cases.
Self Check
Additional Resources
Writing Functions from Graphs
Find the equation of the function graphed above. Then find the value at .
1. Find the value of , the starting point. |
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2. Find the , the growth factor. |
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3. Write the equation of the function. |
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4. Find . |
Try it
Try It: Writing Functions from Graphs
Use the graph below to write the equation of the function. Then find .
Compare your answers:
Here is how to write the exponential function from the graph:
1. Find the value of , the starting point. |
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2. Find the , the growth factor. |
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3. Write the equation of the function. |
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4. Find |