Activity
The cost, in dollars, to produce 1 watt of solar energy is a function of the number of years since 1977, .
From 1977 to 1987, the cost could be modeled by an exponential function . Here is the graph of the function.
1. What is the statement saying about this situation?
Compare your answer:
9 years after 1977 (or in 1986), the cost in dollars for one watt of solar energy was about $6.
2. What is ? What about ? What do these values represent in this context?
Compare your answer:
, and . These values represent the cost in dollars of 1 watt of solar energy in 1981 (4 years after 1977) and halfway through 1980 (3.5 years after 1977).
3. When , what is ? What does that value of represent in this context?
Compare your answer:
2 years after 1977 (in 1979), the cost in dollars of 1 watt of solar energy was $45.
4. By what factor did the cost of 1 watt of solar energy change each year? (If you get stuck, consider creating a table.)
Compare your answer:
or 0.75
Video: Understanding Characteristics of Graphs
Watch the following video to learn more about the characteristics of graphs:
An imaginary line that a function value will not touch or cross is called an asymptote.
The value of the range that the function will never touch is called the horizontal asymptote.
In the function graphed, the horizontal asymptote is .
Self Check
Additional Resources
Reading Exponential Graphs
The graph below describes the amount of caffeine, , in a person’s body hours after an initial measurement of 100 mg.
What does the point mean?
After 10 hours, there is 35 mg of caffeine in a person’s body.
What is the value of when ?
When the caffeine concentration is 80 mg, time is 2 hours, so .
Try it
Try It: Reading Exponential Graphs
Using the graph above, what is the value of , and what does it mean in the context of the situation?
Compare your answer:
Here is how to interpret this exponential graph:
When , the curve crosses at 60, so .
This means that after 5 hours, the person has 60 mg of caffeine in their body.