Answer:
$42,890
Step-by-step explanation:
The standard form for an exponential equation is
where a is the initial amount value and b is the growth rate or decay rate and t is the time in years. Since we are dealing with money amounts AND this is a decay problem, we can rewrite accordingly:
where A(t) is the amount after the depreciation occurs, r is the interest rate in decimal form, and t is the time in years. We know the initial amount (70,000) and the interest rate (.04), but we need to figure out what t is. If the car was bought in 2006 and we want its value in 2018, a total o 12 years has gone by. Therefore, our equation becomes:
or, after some simplification:
First rais .96 to the 12th power to get
A(t) = 70,000(.6127097573)
and then multiply.
A(t) = $42,890