1. Growth and Decay: Integral Exponents
Section 5-1
Growth and Decay: Integral Exponents

2. Exponential Growth and Decay
Look at examples and graphs on page

3. Exponential Growth and Decay Formula
Where is the initial amount, the amount at time t = 0, and r is the growth rate (the percent changed to a decimal) and t is the time. If r > 0, then the initial amount grows exponentially. If -1 < r < 0, then the initial amount decays exponentially.

4. Laws of Exponents Same Bases: 1. 2.
3. If b ≠ 0, 1, or -1, then if and only if x = y.

5. Laws of Exponents Same Exponents: 4. 5.
6. If x ≠ 0, a > 0, and b > 0, then if and only if a = b.

6. Laws of Exponents
Power of a Power: 7.

7. Definition of If Law 1 is to hold for y = 0, then we have
. Since behaves like the number 1, we define it to be 1:
=1 (b ≠ 0)

8. Definition of
If Law 1 is to hold for y = -x and b ≠ 0, then we have Since
and have a product of 1, they are reciprocals of each other. Therefore we define: (x > 0 and b ≠ 0)

9. Additional Example:
In a certain city, the value of a house is increasing at a rate of 16% annually.
Find the value of a $100,000 house in 4 years
In how many years will the value of the house be approximately double what it is now?

10. Example
Simplify each expression.

11. Example
Simplify each expression.

12. Additional Example:
Simplify by using powers of the same base.
a. b.