Exponential Growth vs Decay

Exponential Growth vs Decay

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Growth Function

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

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 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

What is the growth FACTOR of this function?

$$g\left(x\right)=23\left(1.5\right)^x$$  

• 23

• 1
  

• 0.5

• 1.5

Multiple Choice

What is the growth RATE of this function?

$$g\left(x\right)=23\left(1.5\right)^x$$  

• 23

• 1

• 0.5

• 1.5

Multiple Choice

What is the decay RATE of this function?

$$f\left(x\right)=100\left(0.85\right)^x$$  

• 100

• 0.85

• 0.15

• $$\left(1-0.15\right)$$  

Multiple Select

What is the decay FACTOR of this function? Check all that apply.

$$f\left(x\right)=100\left(0.85\right)^x$$  

• 100

• 0.85

• 0.15

• $$\left(1-0.15\right)$$  

Growth and Decay in a Table

• If the constant multiplier is a number between 0 and 1 it is called a DECAY factor.

• (1 - decay rate) = decay factor.

• If the constant multiplier is bigger than 1 it is called a GROWTH factor.

• (1 + growth rate) = growth factor.

Multiple Select

Check all the tables that show exponential DECAY.

Multiple Select

Name the decay FACTOR.  Check all that apply.

• $$\frac{1}{5}$$

• 10

• $$\frac{4}{5}$$

• $$\left(1-\frac{4}{5}\right)$$

Multiple Choice

Name the growth RATE.

• 3

• 2

• $$\left(1+2\right)$$

• 17