1. Algebra 1
Section 8.5

2. Definition
An exponential function is a function of the form f(x) = abx, where b > 0 and b ≠ 1.

3. Example 1 Create a table of ordered pairs for y = 2x. (-3, ⅛) (-2, ¼)
(-1, ½)
(0, 1)
(1, 2)
(2, 4)
(3, 8)

4. Example 1 Create a table of ordered pairs for y = (½)x. (-3, 8)
(-2, 4)
(-1, 2)
(0, 1)
(1, ½)
(2, ¼)
(3, ⅛)

5. Example 1

6. Definition
An asymptote is a line that a graph approaches but never intersects.

7. Example 1
In both functions, the domain is the set of all real numbers, and the range is the set of positive real numbers.

8. Example 2
In this example, we see that the curve of y = a • 2x differs from y = 2x in that for every value of x, the corresponding value of y will be a times its previous value.
The y-intercept will be (0, a).

9. Example 3 y = px Three consecutive reductions of 75%
p = 0.75; y = 0.75x
y = ≈ 0.422
about 42.2% of the original

10. Example 3 y = px Four consecutive enlargements of 150%
p = 1.5; y = 1.5x
y = 1.54 ≈ 5.063
about 506.3% of the original

11. Compound Interest
Most real-world investments involve compound interest.
Compound interest can be modeled with an exponential function.

12. Example 4
The total amount is modeled by the equation y = 10,000(1.05)n, where n is the number of years.
1 year
n = 1
y = 10,000(1.05)1
= $10,500

13. Example 4
The total amount is modeled by the equation y = 10,000(1.05)n, where n is the number of years.
2 years
n = 2
y = 10,000(1.05)2
= $11,025

14. Example 4
The total amount is modeled by the equation y = 10,000(1.05)n, where n is the number of years.
50 years
n = 50
y = 10,000(1.05)50
≈ $114,674
That’s $104,674 in interest!

15. Homework: pp