Exponential FunctionsGrowth and Decay

Graph the following using a table of values.1. y = 2x

2.

3. y = 4x

4.

x y

-2

-1

0

1

2

Exponential Function

An exponential function is a function with the general form y = abx, a≠0, b> 0, and b ≠ 1

Examples:

Growth and Decay

For the function y = abx,

If a>0 and b>1, the function represents exponential growth.

If a>0 and 0<b<1, the function represents exponential decay.

In either case, the y-intercept is (0, a), the domain is all real numbers, the x-axis (y = 0) is the asymptote, and the range is y>0

Identify the following as exponential growth or decay1. y = 5(3x)

2. y = .25 (2x)

3.

4.

Some real life quantities increase or decrease a fixed percent over a time period. The amount y after t years can be modeled by

Exponential ExponentialGrowth Decay

y = a(1 + r)t y = a(1 – r)t

Note: * a is the initial amount * r is the percent increase or decrease

written as a decimal * 1 +r is the growth factor * 1 – r is the decay factor

The value of a car y (in thousands of dollars) can be approximated by the model y = 25(0.85)t , where t is the number of years since the car was new.

a. Tell whether the model represents exponential growth or decay

b. Identify the annual percent increase or decrease in the value of the car

c. Estimate when the value of the car will be $8000

In 2000, the world population was about 6.09 billion. During the next 13 years, the world population increased by about 1.18% each year.

a. Write an exponential model giving the population y (in billions) t years after 2000.

b. Estimate the population in 2005

c. Estimate the year when the world population was 7 billion

The amount y (in grams) of the radioactive isotope chromium-51 remaining after t days is

y = a(0.5)t/28

where a is the initial amount (in grams). What percent of chromium-51 decays each day?

Compound Interest

If an initial deposit, P, is in an account that pays interest at an annual rate, r, compounded n times per year. The amount A in the account after t years is given by:

1nt

rA P

n

You deposit $9000 in an account that pays 1.46% annual interest. Find the balance after 3 years when the interest is compounded quarterly.

1. The amount y (in grams) of the radioactive isotope iodine-123 remaining after t hours is

y = a(0.5)t/13, where a is the initial amount. What percent of iodine-123 decay each hour?

2. You deposit $8600 in an account that pays 1.32% annual interest. Find the balance after 4 years when the interest is compounded monthly.