A national study found that a car's value decreases by 15 percent annually. If the car was purchased for 66,000. How much will the car be worth in 10 years?

Answer:$12,993.71Step-by-step explanation:The formula we want for this is exponential decay which is[tex]A(t)=a(1-r)^t[/tex]where A(t) is the value of the car after the depreciation, a is the initial value of the car, r is the interest rate at which it depreciates in decimal form, and t is the time in years.  We have everything we need to fill in to solve for A(t):[tex]A(t)=66,000(1-.15)^{10}[/tex]We will do some simplifying first:[tex]A(t)=66,000(.85)^{10}[/tex]First raise .85 to the 10th power to getA(t) = 66,000(.1968744043)and then multiply to getA(t) = $12,993.71