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30 June, 07:06

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.

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  1. 30 June, 09:05
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    Step-by-step 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
  2. 30 June, 09:25
    0
    920*1.12^t

    Step-by-step 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.

    You are very welcome!

    :P
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