Exponential Growth & Decay in Real-Life

Chapters 8.1 & 8.2

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

Exponential Growth Model

y = a(1 + r)t

• Can be used for estimating population growth, inflation, and simple interest.

Exponential Growth ModelExample

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 • 1.04t

Exponential Growth Model

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 + )ntrn

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

Exponential Decay ModelExample

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 • .84t

Exponential Decay Model