Exponential Growth and Decay Notes

Exponential Functions: Growth and Decay

Growth Function

The constant multiplier is bigger than 1. Meaning the starting value is keeping 100% of its value and adding some percent.

Growth Function

we have to add the percent as a decimal to 1

1+%=b

Multiple Choice

When will a multiplier be a growth factor?

• When the number is greater than 1

• When the number is greater than or equal to 1

• When the number is less than 1

• When the number is less than or equal to 1

• When the number is equal to 1

Multiple Choice

What is the growth rate for the equation?

y = 200(1.8^x)

• 200

• 1.8

• 80%

Multiple Choice

Is y = 5(1.04)^x growth or decay?

• Growth

• Decay

Multiple Choice

Classify the model as Exponential GROWTH or DECAY.
A=10(1.01)³

• Growth

• Decay

Multiple Select

Which of these functions is a growth function? Check all that apply.

• $$f\left(x\right)=7\left(1.2\right)^x$$

• $$f\left(x\right)=5\left(0.8\right)^x$$

• $$f\left(x\right)=0.5\left(3\right)^x$$

• $$f\left(x\right)=3\left(\frac{4}{3}\right)^x$$

Decay Function

The constant multiplier is between 0 and 1. This number comes from subtracting the decay rate from 100% of the original starting value.

Decay Function

we have to subtract the % as a decimal from 1:

1-%=b

Multiple Choice

When will a multiplier be a decay factor?

• When the number is greater than 1

• When the number is greater than or equal to 1

• When the number is less than 1

• When the number is less than or equal to 1

• When the number is equal to 1

Multiple Choice

What is the decay rate in the following model?

A=1200(.85)⁶

• 1200

• .15

• .85

• 6

Multiple Choice

Is y = 4(.20)^x growth or decay?

• Growth

• Decay

Multiple Choice

Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)⁶

• Growth

• Decay

Starting Amount

The a is the starting amount & the y-intercept. (0, a)

Multiple Choice

In an exponential function, what does the 'a' represent? 

• SLOPE

• RATE OF CHANGE

• Y-INTERCEPT

• COMMON RATIO

Multiple Choice

What is a, the starting term, for the function: f(x) = 300(1.16)^x?

• 300

• 1.16

• .16

• x

Multiple Choice

What is the initial value for the equation?

y = 200(1.8^x)

• 200

• 1.8

• 80%

Multiple Choice

This function represents the number of ants in a colony $$f\left(x\right)=3\ \left(\ 2\right)^x$$

How many ants did you begin with? 

• There was 2 ants

• There was 3 ants

• The equation doesn't tell us

Multiple Choice

Which graphs represent exponential decay?

Multiple Choice

Which graphs represent exponential growth?

Multiple Choice

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

• y = 15(35)^x

• y = 15(1.35)^x

• y = 15(0.35)^x

• y = 35(1.15)^x

Multiple Choice

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

• y=6(0.14)^x

• y=6(1+14)^x

• y=6(1.14)^x

• y=6(0.86)^x

Multiple Choice

A population of 1500 deer decreases by 1.5% per year. At the end of 10 years, there will be approximately 1290 deer in the population.

Which function can be used to determine the number of deer, y, in this population at the end of t years?

• $$y=1500(1-0.015)^t$$

• $$y=1500(0.015)^t$$

• $$y=1500(1+0.015)^t$$

• $$y=1500(1.5)^t$$

Multiple Choice

There were 417 cell phones sold at an electronics store in January. Since then, cell phone sales at this store have increased at a rate of 3.75% per month.

At this rate of growth, which function can be used to determine the monthly cell phone sales x months after January?

• $$f(x)=417(1-0.0375)^x$$

• $$f(x)=417(1-3.75)^x$$

• $$f(x)=417(1+0.0375)^x$$

• $$f(x)=417(1+3.75)^x$$

Multiple Choice

A population of fish starts at 8,000 and decreases by 6% per year.

What is the fish population in 10 years?

• $$14,327$$

• $$4,309$$

• $$839$$

• $$7,680$$

Multiple Choice

Twenty years ago, Mr. Davis purchased his home for $160,000. Since then, the value of the home has increased about 5% per year. How much is the home worth today?

• $176,783.29

• $424,527.63

• $57,357.75

• $532,041,076.80

Multiple Choice

Moody's Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?

• $23,219.72

• $136.72

• $51,710.94

• $16,710.94

Multiple Choice

What is the balance of $6000 compounded annually at a rate of 4% for 10 years?

• $8,881.47

• $7,432.93

• $8,400

• $6,500

Multiple Choice

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?

• 9766

• 9006

• 9765

• 5433

Multiple Choice

An experiment begins with 20 grams of a radioactive isotope. This isotope has a half-life. If y is the mass in grams remaining after x half-lives have elapsed, which equation represents the amount of grams the isotope will weigh after 4 half-lives?

• $$y=20\left(2\right)^4$$  

• $$y=4\left(20\right)^{\frac{1}{2}}$$  

• $$y=20\left(\frac{1}{2}\right)^4$$  

• $$y=20\left(4\right)^{\frac{1}{2}}$$