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Algebra 1

5.15.4 Comparing Linear and Exponential Growth

Algebra 15.15.4 Comparing Linear and Exponential Growth

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1. The linear function g g is defined by g ( x ) = 4 x g ( x ) = 4 x .

a. Show that g ( 3 ) g ( 3 ) and g ( 2 ) g ( 2 ) have a difference of 4.

b. Show that when the input value increases from x x to x + 1 x + 1 , the output values g ( x + 1 ) g ( x + 1 ) and g ( x ) g ( x ) have a difference of 4. Use the '^' symbol to enter an exponent.

2. The exponential function h h is defined by h ( x ) = 4 x h ( x ) = 4 x .

a. Show that h ( 3 ) h ( 3 ) and h ( 2 ) h ( 2 ) have a quotient of 4. Use the '^' symbol to enter an exponent.

b. Show that when the input value increases from x x to x + 1 x + 1 , the output values h ( x + 1 ) h ( x + 1 ) and h ( x ) h ( x ) have a quotient of 4.

Why Should I Care?

A hand holds a tablet displaying stacks of gold coins increasing in height, with the text "Power of Compounding" and example calculations showing how $1,000 grows to $1,210 with repeated 10% interest.

Exponential models can help you understand the power of investment. After two years, this investor made $210 off of an initial investment of $1000 because of the 10% interest rate.

Can you calculate how much money the investor will have made after twenty years?

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