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
