Intro to Exponential Growth & Decay

Intro to Exponential Functions

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Remember

Linear functions have a constant rate of change (as x increases, y increases by constant addition or subtraction.

Exponential functions have a constant multiplier (as x increases, y increases by multiplication).

Multiple Select

Choose all the tables that represent exponential functions.

• a is the starting value, initial value or y-intercept.  This value cannot be 0.

• b is the constant multiplier or growth/decay factor. This value must be greater than 0 but cannot equal 1.

• x almost always represents time.

Multiple Choice

Which variable represents time passed in the function y=ab^x?

• y

• a

• b

• x

Multiple Choice

What is the initial value of the situation represented by f(x)=0.05(2)^x?

• 0.05

• 2

• 0.1

• 1

Multiple Choice

Identify the y-intercept (initial value) in the function y=13(.27)^x

• 0

• .27

• 13

• 3.51

Multiple Choice

Which function has the greatest y-intercept?

• $$y=3\cdot4^x$$

• $$y=4\cdot3^x$$

• $$y=1\cdot5^x$$

• $$y=5\cdot2^x$$

Multiple Choice

Choose the correct equation for the table

• $$y=4\left(5\right)^x$$

• $$y=5\left(20\right)^x$$

• $$y=5\left(4\right)^x$$

• $$y=5\left(15\right)^x$$

Evaluating Functions

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Multiple Choice

Use the function, M =.05(2)^t, where M is the amount of money you have after t days.

How much money will you have after 14 days?

• $ 819.20

• $ 8,192.00

• $ 1.40

• $ 819.02

Multiple Choice

Use the function, N = 14,000(.96)^t. Where N is the number of employees and t is the number of years.

How many employees will there be after 3 years?

• 14,000 employees

• 12,386 employees

• 40,360 employees

• 15,748 employees

Growth

A function grows when the starting value (a) is greater than 0 and the constant multiplier (b) is greater than 1.

In a growth function the constant multiplier might also be called a growth factor.

Decay

A function decays when the starting value (a) is greater than 0 and the constant multiplier (b) is between 0 and 1.

In a decay function the constant multiplier might also be called a decay factor.

Multiple Choice

What does this graph represent?

• Exponential Decay

• Exponential Growth

Multiple Choice

What does the graph represent?

• Exponential Decay

• Exponential Growth

Multiple Choice

Is the graph exponential growth or decay?

• Exponential growth
• Exponential decay

Multiple Choice

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

• Exponential Growth
• Exponential Decay
• Linear
• None of the above

Open Ended

Using complete sentences, tell me 2 things you learned and one thing you wish I knew.

Multiple Choice

What type of function is f(x)=2(1/7)^x ?

• Exponential Growth

• Linear

• Exponential Decay

• None of the Above