y = (1)2 · A261ExpGrowthAndDecay.notebook November 06, 2017 HW43 61 P300 #47,9,15,16,1922 Please...

A261ExpGrowthAndDecay.notebook November 06, 2017

Algebra 2

P36 61 Exponential Growth and Decay Functions

Exponential Functionsx is a real numbera≠0, b > 0, b ≠ 1 y = abx

y = (2)3x


If b > 1,b is the Growth Factory = (1)2x

If 0 < b < 1,b is the Decay Factory = (1).5x

Growth and Decay y = abx


Graph each function. f (x) = 2(4)x f (x) = 2


Tell whether each function represents exponential growth or exponential decay. Then graph the function.

a. y = 2x b. y =


Determine whether each function represents exponential growth or exponential decay.

Identify the percent rate of change.

a. y = 5(1.07)t b. f (t) = 0.2(0.98)t

Population Growth ExampleIn 2000, the annual rate of increase in the U.S. population was about 1.24%. Suppose the rate of increase continues to be 1.24%. Write a function to model U.S. population growth, in millions, after the year 2000.

Growth Factor (b = 1 + rate of growth)

(In 2000, there were 281 million people in the U.S.)(2000 would be year Zero)


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 growth model giving the population y (in billions) t years after 2000. Estimate the world population in 2005.

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

DepreciationLoss of Value over Time

Growth/Decay Factor (b = 1 +/ (r) rate of growth)r = Final Value Initial Value

Initial Value

The initial value of a car is $20,000. After one year the value of the car is about $17,000. Write an Exponential Function to model the situation. Find the value of the car in year 6.

y = abx


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 exponential 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.

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


HW43 61 P300 #47,9,15,16,1922

Please put your name and class period at the top of the homework. Also include the homework number.

If b > 1,b is the Growth Factory = (1)2x

If 0 < b < 1,b is the Decay Factory = (1).5x

Growth and Decay y = abx


1. y = 4x 2. y =

3. f (x) = (0.25)x 4. f (x) = (1.5)x

Tell whether the function represents exponential growth or exponential decay. Then graph the function.

Basketball TournamentDecay Example

64 teamsSingle Elimination Tournament

y = abx

y = (1)2 · A261ExpGrowthAndDecay.notebook November 06, 2017 HW43 61 P300 #47,9,15,16,1922 Please...

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