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. Tiles 920(1.03) is the number of cars multiplied by 1.03. The initial number of cars serviced is 920. The growth rate is 1.03. The compound periods multiplied by the number of years is 4t. The growth factor is represented by 1.03. The quarterly rate of growth is 0.03 or 3%. Pairs Coefficient arrowBoth Base arrowBoth Rate arrowBoth Exponent arrowBoth

Answer 1

Answer: The required function is f(t)= $920[1.03]^{4t}$

where, 920 is the initial number of cars, the growth rate is 0.03, growth factor is 1.03, 4 t is number of periods and The quarterly rate of growth is 0.03 or 3%

Step-by-step explanation:

Here,  car repair center services 920 cars in 2012 and the number of cars serviced increases quarterly at a rate of 12% per year after 2012.

Since, rate is 12 % annually, therefore, rate in quarterly = 12/4= 3%

If we have to find out the number of cars after t years then total number of quarters = 4t

Thus, the cars after t years,

f(t) = $920[1+3/100]^{4t}$     ( by the formula $A= P(1+r/100)^t$)

or  f(t)= $920[1.03]^{4t}$,

where 1.03 is the growth factor of the above exponential function.

And, initially t =0 therefore, f(0)= 920  which is the initial value of car.