Depreciation A car sells for $30,000. The car depreciates such that each year it is worth 4 5 of its value from the previous year. Find a model for the value V of the car after t years. Sketch a graph of the model and determine the value of the car 5 years after it is purchased.

Q: Expert Answer

To determine To calculate: The model for the value V and the price of a car after 5 years of purchase and also sketch the graph of the model, if the selling price of car is $ 30 , 000 and the value depreciates in such a way that each passing year its worth is 4 5 of value from the previous year. Explanation Given information: The selling price of car is $ 30 , 000 and the value depreciates in such a way that each passing year its worth is 4 5 of its value from the previous year. Calculation: Consider the provided information, The selling price of car is $ 30 , 000 and the value depreciates in such a way that each passing year its worth is 4 5 of value from the previous year. So, the model is given by V ( t ) = 30 , 000 ( 4 5 ) t . Substitute t = 1 in the function V ( t ) = 30 , 000 ( 4 5 ) t , V ( 1 ) = 30 , 000 ( 4 5 ) 1 = 24 , 000 Substitute t = 2 in the function V ( t ) = 30 , 000 ( 4 5 ) t , V ( 2 ) = 30 , 000 ( 4 5 ) 2 = 19 , 200 Substitute t = 3 in the function V ( t ) = 30 , 000 ( 4 5 ) t , V ( 3 ) = 30 , 000 ( 4 5 ) 3 = 15 , 360 Substitute t = 4 in the function V ( t ) = 30 , 000 ( 4 5 ) t , V ( 4 ) = 30 , <

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Calculus: An Applied Approach (Min...

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Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition

Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

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Answer 3

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To determine

To calculate: The model for the value V and the price of a car after 5 years of purchase and also sketch the graph of the model, if the selling price of car is $30,000 and the value depreciates in such a way that each passing year its worth is 45 of value from the previous year.

Explanation of Solution

Given information:

The selling price of car is $30,000 and the value depreciates in such a way that each passing year its worth is 45 of its value from the previous year.

Calculation:

Consider the provided information,

The selling price of car is $30,000 and the value depreciates in such a way that each passing year its worth is 45 of value from the previous year.

So, the model is given by V(t)=30,000(45)t.

Substitute t=1 in the function V(t)=30,000(45)t,

V(1)=30,000(45)1=24,000

Substitute t=2 in the function V(t)=30,000(45)t,

V(2)=30,000(45)2=19,200

Substitute t=3 in the function V(t)=30,000(45)t,

V(3)=30,000(45)3=15,360

Substitute t=4 in the function V(t)=30,000(45)t,

V(4)=30,<

Depreciation A car sells for $30,000. The car depreciates such that each year it is worth 4 5 of its value from the previous year. Find a model for the value V of the car after t years. Sketch a graph of the model and determine the value of the car 5 years after it is purchased.

Calculus: An Applied Approach (Min...

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Calculus: An Applied Approach (Min...