1. College Algebra Chapter 4 Exponential and Logarithmic Functions
Section 4.2
Exponential Functions

2. 1. Graph Exponential Functions
2. Evaluate the Exponential Function Base e
3. Use Exponential Functions to Compute Compound Interest
4. Use Exponential Functions in Applications

3. Graph Exponential Functions
Previously:
Now:

4. Graph Exponential Functions
Let b be a constant real number such that b > 0 and b ≠ 1.
Then for any real number x, a function of the form
is called an exponential function of base b.

5. Example 1:
Graph the function.

6. Example 2:
Graph the function.

8. Example 3:
Graph the function.

9. Example 3 continued: Parent function: If h > 0, shift to the right.
If h < 0, shift to the left.
Parent function:
If a < 0 reflect across the x-axis.
Shrink vertically if 0 < |a| < 1.
Stretch vertically if |a| > 1.
If k > 0, shift upward.
If k < 0, shift downward.

11. 1. Graph Exponential Functions
2. Evaluate the Exponential Function Base e
3. Use Exponential Functions to Compute Compound Interest
4. Use Exponential Functions in Applications

12. Evaluate the Exponential Function Base e
e is a universal constant (like the number ) and an irrational number.
e ≈

13. Examples 4 – 7:
Evaluate. Round to 4 decimal places. 4. 5. 6. 7.

14. Example 8:
Graph the function.

16. 1. Graph Exponential Functions
2. Evaluate the Exponential Function Base e
3. Use Exponential Functions to Compute Compound Interest
4. Use Exponential Functions in Applications

17. Use Exponential Functions to Compute Compound Interest
Suppose that P dollars in principle is invested (or borrowed) at an annual interest rate r for t years. Then:
Amount of simple interest I (in $)
Amount A (in $) in the account after t years and n compounding periods per year.
Amount A (in $) in the account after t years under continuous compounding.

18. Example 9:
Suppose that $15,000 is invested with 2.5% interest under the following compounding options. Determine the amount in the account at the end of 7 years for each option.
a) Compounded annually

19. Example 9 continued: b) Compounded quarterly
c) Compounded continuously

21. 1. Graph Exponential Functions
2. Evaluate the Exponential Function Base e
3. Use Exponential Functions to Compute Compound Interest
4. Use Exponential Functions in Applications

22. Example 10:
Weapon-grade plutonium is composed of approximately 93% plutonium-239 (Pu-239). The half-life of Pu-239 is 24,000 years. In a sample originally containing 0.5 kilograms, the amount left after t years is given by
Evaluate the function for the given values of t and interpret the meaning in context.

23. Example 10 continued: a) b)

24. Example 11:
A 2010 estimate of the population of Mexico is 111 million people with a projected growth rate of 0.994% per year. At this rate, the population P(t) (in millions) can be approximated by
where t is the time in years since 2010.

25. Example 11 continued: