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A new car is purchased for 19900 dollars. The value of the car depreciates at 7.5% per year. What will the value of the car be, to the nearest cent, after 8 years?

Respuesta :

calculista

Answer:

[tex]\$10,665.64[/tex]  

Step-by-step explanation:

we know that

The  formula to calculate the depreciated value  is equal to  

[tex]V=P(1-r)^{x}[/tex]  

where  

V is the depreciated value  

P is the original value  

r is the rate of depreciation  in decimal  

x  is Number of Time Periods  

in this problem we have  

[tex]P=\$19,900\\r=7.5\%=0.075\\x=8\ years[/tex]

substitute the values in the formula

[tex]V=\$19,900(1-0.075)^{8}=\$10,665.64[/tex]  

turnerkddp3hrfz

Answer: The answer is 10665.64

Step-by-step explanation:

Exponential Functions:

y=ab^x

A= starting value = 19900

r=rate = 7.5%=0.075

Exponential Decay:

b=1-r=1-0.075=0.925  

Write Exponential Function:

y=19900(0.925)^x

Plug in time for x:

y=19900(0.925)^8

y= 10665.6404317  

Evaluate

y≈10665.64

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