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As a car ages, its value decreases. The value of a particular car with an original purchase price of $27,000 is modeled by the following function, where 𝑐 is the value at time 𝑡, in years.𝑐⁡(𝑡)=27,000⁢(1-0.21)𝑡What is the value of the car when it is 4 years old?The value of the car after 4 years is $What is the total depreciation amount after 5 years?After 5 years, the total depreciation amount is $

Question

As a car ages, its value decreases. The value of a particular car with an original purchase price of 27,000ismodeledbythefollowingfunction,where𝑐isthevalueattime𝑡,inyears.𝑐⁡(𝑡)=27,000⁢(1−0.21)𝑡Whatisthevalueofthecarwhenitis4yearsold?Thevalueofthecarafter4yearsis27,000 is modeled by the following function, where 𝑐 is the value at time 𝑡, in years.𝑐⁡(𝑡)=27,000⁢(1-0.21)𝑡What is the value of the car when it is 4 years old?The value of the car after 4 years is What is the total depreciation amount after 5 years?After 5 years, the total depreciation amount is $

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Solution

To find the value of the car when it is 4 years old, we substitute t=4 into the function:

c(4) = 27,000 * (1 - 0.21)^4

First, calculate the value of (1 - 0.21)^4 = 0.59 (approximately)

Then, multiply this by 27,000 to get the value of the car after 4 years:

c(4) = 27,000 * 0.59 = $15,930

So, the value of the car when it is 4 years old is $15,930.

To find the total depreciation amount after 5 years, we first need to find the value of the car after 5 years:

c(5) = 27,000 * (1 - 0.21)^5

First, calculate the value of (1 - 0.21)^5 = 0.47 (approximately)

Then, multiply this by 27,000 to get the value of the car after 5 years:

c(5) = 27,000 * 0.47 = $12,690

The total depreciation amount is the original price minus the value after 5 years:

Depreciation = 27,000 - 12,690 = $14,310

So, after 5 years, the total depreciation amount is $14,310.

This problem has been solved

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