Homework Questions!

Unit 3

Exploring Exponential Models

An exponential function is a function with the general form of:

y = abx

where x is a real number, a ≠ 0, b > 0, and b ≠ 1.

Graphing Exponential Equations y = 2x

x y

-3

-2

-1

0

1

2

3

EXPONENTIAL GROWTH y = a • bx time

initial amount growth factor (1+r)

Ex. The population of the US in 1994 was about 260

million with an average annual rate of increase

of about 0.7%. 1. Write a function to model this population.

2. What was the population in 2006?

Modeling growth

• The bear population increases at a rate

of 2% per year. There are 1573 bears this year. Write a function that models the bear population. How many bears will there be in 10 years?

Exponential Decay

y = a(1-r)t

Ex. 1. Suppose you want to buy a used car that costs $11,800. The expected depreciation of the car is 20% per year. Estimate the depreciated value of the car after 6 years.

More Decay…..

Ex. 2. The population of a certain animal species decreases at a rate of 3.5% per year. You have counted 80 animals in the habitat. Write the equation.

Ex: Analyzing a Function

Without graphing, determine whether the function y = 14(0.95)x represents exponential growth or exponential decay.

Without graphing, determine whether the function y = 0.2(5)x represents exponential growth or exponential decay.

An asymptote is a line that a graph approaches as x or y increases in absolute value.

Ex: Graphing Exponential Decay

y = 24(1/3)x

Identify.

• Horizontal Asymptote

• Domain

• Range

x y

-3

-2

-1

0

1

2

3

Example 5b Graphing Exponential Decay

y = 100(0.1)x

Identify.

• Horizontal asymptote

• Domain

• Range

x y

-3

-2

-1

0

1

2

3

Example 2 Translating y = abx

y =8(1/2)x y = 8(1/2)x+2 +3

Example 2b Translating y = abx

y =2(3)x-1 + 1 y = -3(4)x+1 +2

Half-life!

What does that mean?

• The half-life is the amount of time it takes for half of the atoms in a sample to decay.

A = A0(1/2)1

Half life* t

Example 3 Real World Connection

A hospital prepares a 100-mg supply of

technetium-99mg which has a half-life of 6 hours. Write an exponential function to find the amount of technetium-99mg that remains after 75 hours.

Another Half-Life?

• Arsenic-74 is used to locate brain tumors. It has a half-life of 17.5 days. Write an exponential decay function for a 90-mg sample. Use the function to find the amount remaining after 6 days.

Classwork/homework

• Worksheet