1. Exponential Growth & Decay in Real-Life Chapters 8.1 & 8.2

2. Exponential Growth Models When a real-life quantity increases by a fixed percent each year (or other period of time), the amount, y, after t years can be modeled by the equation: y = a(1 + r) t a is the initial amount, r is the percent increase Growth Factor

3. Exponential Growth Model y = a(1 + r) t Can be used for estimating population growth, inflation, and simple interest.

4. Exponential Growth Model Example In 1990, the cost of tuition at a state university was $4300. During the next 8 years, the tuition rose 4% each year. a)Write a model that gives the tuition y (in dollars) t years after 1990. b)Graph the model. y = 4300 1.04 t

5. Exponential Growth Model

6. Compound Interest Simple Interest is paid only the initial investment, which is called the principle Compound Interest is paid on the principle AND on previously earned interest. The principle, P, in an account, A, that pays interest at an annual rate r, compounded n times per year can be modeled A = P(1 + ) nt rnrn

7. Exponential Decay Models When a real-life quantity Decreases by a fixed percent each year (or other period of time), the amount, y, after t years can be modeled by the equation: y = a(1 – r) t a is the initial amount, r is the percent increase Decay Factor

8. Exponential Decay Model Example You buy a new car for $24,000. The value y of the car decreases by 16% a)Write a model that gives the tuition y (in dollars) t years after 1990. b)Use the model to estimate the value of your car after 2 years. y = 24,000.84 t

9. Exponential Decay Model