Question

A car repair center services 920 cars in 2012. The number of cars serviced increases quarterly at a rate of 12% per year after 2012. Create an exponential expression to model the number of cars serviced after t years. Then, match each part of the exponential expression to what it represents in the context of the situation. The quarterly rate of growth is 0.03 or 3%. The growth rate is 1.03. The growth factor is represented by 1.03. The compound periods multiplied by the number of years is 4t. 920(1.03) is the number of cars multiplied by 1.03. The initial number of cars serviced is 920. Coefficient arrowRight Exponent arrowRight Rate arrowRight Base arrowRight

Answer 1

Answer:

N=920 (1+0.03)^4t

where N=number of cars serviced after t years

Step-by-step explanation:

Apply the compound interest equation

N=P( 1+r/n)^nt

where N ending number of cars serviced , P is the number of cars serviced in 2012, r is the interest rate, n is the number of compoundings per year, and t is the total number of years.

Matching parts of the exponential function

Initial number of cars serviced=920

The quarterly rate of growth = if interest is compounded quarterly, n=4

r=12% ÷ 4 = 0.03 or 3%

The growth rate is given by (1 +r/n) = 1+0.03 = 1.03

number of compoundings for t years= nt= 4t

The compound period multiplied by the number of years = 920(1.03)^4t