Exponential Functions: Growth and Decay

Exponential Functions: Growth and Decay

By Carson Costa

Multiple Choice

Use desmos.com/calculator to determine which table matches the function 

$$f\left(x\right)=2\left(3\right)^x$$  

Growth Function

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

Multiple Select

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

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

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

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

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

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

Use desmos.com/calculator to determine which table matches the function 

$$h\left(x\right)=12\left(\frac{1}{3}\right)^x$$  

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.

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

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

• y=5000(0.7)^x

• y=30(5000)^x

• y=5000(1.3)^x

• y=5000x^x

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

Exponential Functions

Fill in the Blank

If the functions is growing at a rate of 2.7%, the b value is _______.

f(x) = 2^x

(Parent Function)

• g(x) = 2^x + 3 represents a vertical shift up 3

• h(x) = 2^x - 3 represents a vertical shift down three

f(x) = -2^x

​If a or b are negative, it causes an x-axis reflection.

​x	​y
-2​	​-1/4
​-1	-1/2​
​0	​-1
​1	​-2
​2	-4​