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.

Answer 1

920*1.12^t

Explanation:

Every year, we see that it goes up 12%.

12% in decimal form is 0.12.

Let's say we have "x" amount of cars one year. The next year, the number of cars will increase by 12%. 0.12x is added on after one year.

So in total, at the beginning of a new year, the number of cars is 0.12x+x = 1.12x.

In this case, we have 920 cars. So if every year the number of cars is multiplied by 1.12, then in "t" years we will have 920*(1.12)^t. We multiply by 920 because that's the current number of cars, and we add the ^t because we multiply by 1.12 every year.

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Answer 2

Explanation:

The exponential model for the number of cars serviced after t years would be

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

Where

A represents the total number of cars serviced after t years

P represents the initial number of cars serviced at the car repair center.

r represents the rate at which the number of cars serviced at the car repair center increased per year.

n represents the number of times that the number if cars increased per year.

t represents the number of years.

From the given information,

The car repair center serviced 920 cars in 2012. So P = 920

The number of cars serviced increases quarterly at a rate of 12% per year after 2012. This means that n = 4 and r = 12% = 12/100 = 0.12

The exponential model becomes

A = 920(1 + 0.12/4)^4t

A = 920(1.03)^4t