1. Introduction to Solving Exponential and Logarithms

Introduction to Solving Exponential and Logarithms

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Page 5 #1

What exponential function models the value of a new car after t years if the car initially costs $20,000 and depreciates at a rate of 8% each year?

• $$Value=\left(20000\right)\left(1+.08\right)^t$$

• $$Value=\left(20000\right)\left(1-.08\right)^t$$

• $$Value=\left(20000\right)\left(1.08\right)^t$$

• $$Value=\left(20000\right)\left(.92\right)^t$$

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Page 5 #2

What exponential function models the value of a new car after t years if the car initially costs $16,000 and depreciates at a rate of 7% each year?

• $$Value=\left(16000\right)\left(1+.07\right)^t$$

• $$Value=\left(16000\right)\left(1-.07\right)^t$$

• $$Value=\left(16000\right)\left(1.07\right)^t$$

• $$Value=\left(16000\right)\left(.93\right)^t$$

Fill in the Blanks

Page 5 #3

Fill in the blank below to create an equation for when the cars will have the same value.

Hint: same value means what math symbol?

$20000\left(.92\right)^t$

$16000\left(.93\right)^t$

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Page 5 #4

The solution to the equation $$20000\left(0.92\right)^t=16000\left(0.93\right)^t$$ gives you the time at which the cars will have the same value. Find the solution to this equation using tables.

Hint: Click the rectangle where is f(x) and g(x) the closest to the same number.

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Page 5 #5

How many years will the cars have the same value? What is the value of the car then?



It will take ​

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years. The value will be ​

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Page 6 #6

Solve the equation $$100e^{0.06t}=200e^{0.055t}$$ using tables.

Hint: Click the rectangle where is f(x) and g(x) the closest to the same number.

Fill in the Blanks

Page 6 #6

Solve the equation $100e^{0.06t}=200e^{0.055t}$ using tables.

Hint: Where is f(x) and g(x) the closest to the same number.

x=

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Page 6 #7

Solve the equation $$90e^{0.005t}=500e^{0.025t}$$ using tables.

Hint: Click the rectangle where is f(x) and g(x) the closest to the same number.

Fill in the Blanks

Page 6 #7

Solve the equation $90e^{0.005t}=500e^{0.025t}$ using tables.

Hint: Where is f(x) and g(x) the closest to the same number.

x=