1. College Algebra Chapter 4 Exponential and Logarithmic Functions
Section 4.2
Exponential Functions
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2. Concepts Graph Exponential Functions
Evaluate the Exponential Function Base e
Use Exponential Functions to Compute Compound Interest
Use Exponential Functions in Applications

3. Concept 1 Graph Exponential Functions

4. Graph Exponential Functions (1 of 2)
Previously:
Now:

5. Graph Exponential Functions (2 of 2)
Exponential Function: 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.

6. Example 1 (1 of 2)
Graph the function.
Solution:

7. Example 1 (2 of 2)

8. Example 2 (1 of 2)
Graph the function.
Solution:

9. Example 2 (2 of 2)

10. Skill Practice 1
Graph the functions.

11. Example 3 (1 of 4)
Graph the function.
Solution:

12. Example 3 (2 of 4)

13. Example 3 (3 of 4) Parent function: Where in, ab:
If a<0 reflect across the x-axis.
Shrink vertically if 0< |a| < 1.
Stretch vertically if |a| > 1.
x – h:
If h > 0, shift to the right.
If h < 0, shift to the left.

14. Example 3 (4 of 4) k: If k > 0, shift upward.
If k < 0, shift downward.
Where,
x + 1: 1 to left
-2: reflect across x-axis
1: 1 up

15. Skill Practice 2
Graph.

16. Concept 2 Evaluate the Exponential Function Base e

17. Evaluate the Exponential Function Base e
e is a universal constant (like the number ) and an irrational number.
Approaches a constant value that we call e e ≈

18. Examples 4 – 7
Evaluate. Round to 4 decimal places.

19. Example 8 (1 of 2)
Graph the function.
Solution:

20. Example 8 (2 of 2)

21. Skill Practice 3

22. Concept 3 Use Exponential Functions to Compute Compound Interest

23. 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: I = Prt: Amount of simple interest I (in $)
Amount A (in $) in the account after t years under continuous compounding.
Amount A (in $) in the account after t years and n compounding periods per year.

24. Example 9 (1 of 2)
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.
Compounded annually
Solution:

25. Example 9 (2 of 2) Compounded quarterly Solution:
Compounded continuously
Solution:

26. Skill Practice 4
Suppose that $8000 is invested and pays 4.5% per year under the following compounding options.
Compounded annually
Compounded quarterly
Compounded monthly
Compounded daily
Compounded continuously
Determine the total amount in the account after 5 year with each option.

27. Concept 4 Use Exponential Functions in Applications

28. Example 10 (1 of 3)
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.

29. Example 10 (2 of 3)
A(24,000)
Solution:

30. Example 10 (3 of 3)
A(72,000)
Solution:

31. Example 11 (1 of 2)
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.

32. Example 11 (2 of 2)
Evaluate P(4) and interpret its meaning in the context of this problem.
Solution:
In 2014 population of Mexico will be ≈ 115 million.
Evaluate P(75) and interpret its meaning in the context of this problem.
Solution:
In 2085 population of Mexico will be ≈ 233 million.

33. Skill Practice 5
Cesium-137 is a radioactive metal with a short half-life of 30 yr. In a sample originally having 2 g of cesium-137, the amount A(t) (in grams) of cesium-137 present after t years is given by
How much cesium-137 will be present after
30 year?
60 year?
90 year?