6.2 Exponential Functions

An exponential function of form f(x) =b^x includes the points (2, 16), (3, 64), and (4,256). What is the value of b? Recall b is your constant multiplier.

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CCSS.HSF.LE.A.2

The exponential function f(x)=2^x increases as x increases. Do all exponential functions of the form

b^x behave this​ way? Use algebraic reasoning to support your answer.

• Yes. Exponential functions increase for all values of b.

• Yes. Exponential functions increase when

  0<b<1.

• No. Exponential functions decrease when

  0<b<1.

• No. Exponential functions decrease when

  b>1.

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CCSS.HSF-IF.C.7E

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CCSS.HSF-IF.C.7E

Find the x intercept.

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• 1

• 2

• There is no x-intercept.

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CCSS.HSF-IF.C.7E

Find the y intercept. Write your answers in ordered pair form with no spaces.

Tags

CCSS.HSF-IF.C.7E

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CCSS.HSA.CED.A.2

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CCSS.HSA.CED.A.2

Write an exponential equation for the table.

Use format: y=ab^x

Answer explanation

y=ab^x

1) Find the factor that y increases by (1.18) Round to 2 places.

2) Since x increases by 2, b^2=1.18. Find b. Round to 3 places. (b=1.086)

3) Now that we know b, use any coordinate pair from the table to put into the equation and find a. 1.26=a(1.086)^4 (a=0.906)

4) Now that you've found a, rewrite the equation using the a and b values you found.

y=0.906(1.086)^x

Tags

CCSS.HSF.LE.A.2

Use the graph shown to the left to write an exponential function to model the situation.

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Answer explanation

y=ab^x

a is your initial value

b is your constant rate

Tags

CCSS.HSF.LE.A.2

Write an exponential equation for the data in the table.

Use (^) for the exponent.

Answer explanation

The starting value (a) is 1, which doesn't need to be represented in the equation. The constant value (b) is 6 (notice that each y-value is 6 times larger than the prior value).

Tags

CCSS.HSF.LE.A.2