Answered

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A car had a value of $10,000 and depreciates at a rate of 7% a year. What is the cars value after 3 years.​

Sagot :

Luv2Teach

Answer:

Step-by-step explanation:

The exponential decay function is

[tex]v(t)=a(b)^t[/tex] where a is the initial value of the car, b is the rate of decay, and t is the time in years. Our rate of decay can also be written as (1 - r) where r is the depreciation in decimal form. Our equation looks like this:

[tex]v(t)=10000(1-.07)^t[/tex] which simplifies to

[tex]v(t)=10000(.93)^t[/tex] Now we can solve our problem for any number of years you'd like. We've been tasked to find the value of the car after 3 years, so:

[tex]v(t)=10000(.93)^3[/tex] which simplifies a bit to:

[tex]v(t)=10000(.804357)[/tex] so

v(t) = 8043.57

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