Exponential Growth and Decay

Exponential Growth and Decay

Review: How to convert percent to decimals

Simply move decimal twice to the left to convert to decimal

Multiple Choice

Convert 70% to a decimal.

• 0.70

• 0.07

• 0.007

• 0.0007

Multiple Choice

Change 16% into a decimal.

• 16.0

• 0.016

• 0.16

• 0.0016

Multiple Choice

Convert 1.65% to a decimal.

• 165.0

• 0.00165

• 0.165

• 0.0165

Multiple Choice

Convert 3% to decimal.

• 0.03

• 0.003

• 3.0

• 30.0

Exponential Growth Graph

 $y=a\left(1+r\right)^x$  

 $y=a\left(1+r\right)^x$  

        or
 $y\ =a\left(b\right)^x$  

• a = initial value (also the y-int)

• r = growth rate % (sometimes given as a percent, must convert to decimal)

• x = number of time intervals

• y = total amount

• b = common ratio or constant ratio (b > 1 to be exponential growth)

Multiple Choice

Is the following an example of Exponential Growth?

 $y=2\left(1.5\right)^x$   Note: is b > 1

• Yes

• No

Multiple Choice

Is the following an example of Exponential Growth?

 $y=2\left(\frac{1}{3}\right)^x$   

• Yes

• No

Multiple Choice

Is the following an example of Exponential Growth?

 $y=2\left(\frac{4}{3}\right)^x$   

• Yes

• No

Multiple Choice

Is the following an example of Exponential Growth?

 $y=2\left(0.4\right)^x$   

• Yes

• No

Multiple Choice

Is the following an example of Exponential Growth?

 $y=2\left(x\right)^2$   

• Yes

• No

Exponential Growth Word Problems -

How do we find y? (total amount)

Multiple Choice

The population of turtles is doubling every 6 months. If there are 400 turtles now, how many will there be in 2 years? (Choose equation)

• y = 400(2)²

• y = 400(2)⁴

• y = 400(2)⁶

• y = 400 + 2(8)

Multiple Choice

The population of turtles is doubling every 6 months. If there are 400 turtles now, how many will there be in 2 years? (Choose equation)

• 1,600 turtles

• 6,400 turtles

• 25,600 turtles

• 416 turtles

Multiple Choice

Twenty years ago, Mr. Davis purchased his home for $160,000. Since then, the value of the home has increased by 5% per year.  Which would help you find the worth of the house today?

•  $y=160\left(1+.05\right)^{20}$  

•  $y=160,000\left(1.05\right)20$  
  

•  $y=160,000\left(1.5\right)^{20}$  
  

•  $y=160,000\left(1.05\right)^{20}$  

Multiple Choice

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

• $176,783.29

• $57,357.75

• $424,527.63

• $532,041,076.80

Multiple Choice

The original value of a painting is $1,400, and the value increases by 9% each year. Write an exponential growth function to model this situation.

• y=1,400(1.09)^x

• y=1,400(.91)^x

• y=1.09(1,400)^x

• y=1.09^x

Multiple Choice

The original value of a painting is $1,400, and the value increases by 9% each year. Write an exponential growth function to model this situation. How much is it worth in 5 years?

• $2,154

• $874

• $2,698

• $1,539

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

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. Approximately how long will it be in 4 weeks?

• 8 in

• 12 in

• 7 in

• 10 in

Exponential Decay

Exponential Decay Graph

 $y=a\left(1-r\right)^x$  

Multiple Choice

Is this an example of an exponential graph?

• yes, its an exponential growth

• yes, its an exponential decay

• no

Multiple Choice

Is this an example of an exponential graph?

• yes

• no

Multiple Choice

What type of exponential graph is this?

• Exponential Growth

• Exponential Decay

Multiple Choice

What type of exponential graph is this?

• Exponential Growth

• Exponential Decay

• Neither

 $y=a\left(1-r\right)^x$  

        or
 $y\ =a\left(b\right)^x$  

• a = initial value (also the y-int)

• r = growth rate % (sometimes given as a percent, must convert to decimal)

• x = number of time intervals

• y = total amount

• b = common ratio or constant ratio (b < 1 to be exponential decay)

Multiple Choice

True or False:

In an exponential decay equation, b must be less than 1.

• True

• False

Multiple Select

Select all that apply:

Which of the following are examples of Exponential Decay?

• $y=2\left(1-.04\right)^x$

• $y=5\left(.8\right)^x$

• $y=\left(\frac{4}{3}\right)^x$

• $y=3\left(\frac{1}{3}\right)^x$

Exponential Decay Word Problems -

How do we find y? (total amount)

Multiple Choice

Classify the model as Exponential GROWTH or DECAY.

A=1200(.85)⁶

• Growth

• Decay

Multiple Choice

Classify the model as Exponential GROWTH or DECAY.

A=10(1.01)³

• Growth

• Decay

Multiple Choice

What type of function is y = 7(5/4)^x?

• Growth

• Decay

• Linear

• None

Multiple Choice

A population of 2200 beetles is too large to sustain and decreases in population each month at a rate of 5%. How would you write your decay factor, b?   **Note**  $b=\left(1-r\right)$   

• -5

• .95

• -.05

• .05

Multiple Choice

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. How would you write your decay factor, b?

• 1.30

• .70

• -.30

• .30

Multiple Choice

Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 15%. How much will the printer be worth in 8 years?

• $9537.17

• $51,710.94

• $1136.72

• $16,710.94

Multiple Choice

An adult takes 400 mg of ibuprofen. Each hour, the amount of ibuprofen in the person’s system decreases by about 29%. How much ibuprofen is left after 6 hours?

• 284 mg

• 116 mg

• 1843 mg

• 51 mg

Multiple Choice

The population of Bloom Falls, Mass. (population 937) is slowly moving to a bigger city.

Every year the population drops by 4.5%. What is the population after 3 years?

• 1,069 people

• 816 people

• 894 people

• 854 people

Please download Desmos on your phones or go to www.desmos.com/calculator on computer

You will use this calculator when finding x (time) in a word problem.

How do we find x (time)?

Multiple Choice

A certain drug decays at a rate of 15% per hour. If the initial dose is 500mg and it is not safe to drive until there is only 50mg left in a person's system, how long will it be until it is safe for someone to drive?

• 6 hrs

• 8 hrs

• 12 hrs

• 14 hrs