In 1990, the cost of tuition at a large Midwestern university was $95 per credit hour. In 1999, tuition had risen to $221 per credit hour. D

Question

In 1990, the cost of tuition at a large Midwestern university was $95 per credit hour. In 1999, tuition had risen to $221 per credit hour. Determine a linear function C(x) to represent the cost of tuition as a function of x, the number of years since 1990 C(x)= *answer here*

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Khang Minh 4 months 2021-09-04T16:59:28+00:00 1 Answers 5 views 0

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    2021-09-04T17:00:39+00:00

    Answer:

    The cost of tuition as a function of x, the number of years since 1990, is C(x)= 14*(x-1990) + 95

    Step-by-step explanation:

    A linear function is a polynomial function of the first degree that has the following form:

    y= m*x + b

    where

    • m is the slope of the function
    • n is the ordinate (at the origin) of the function

    So, in this case: C(x)= m*( x-1990) + b where x is the number of years since 1990.

    Given the coordinates of two points, it is possible to determine the slope m of the line from them using the following formula:

    m=\frac{y2 - y1}{x2 - x1}

    In this case, you know that in 1990, the cost of tuition at a large Midwestern university was $95 per credit hour. And in 1999, tuition had risen to $221 per credit hour. So:

    • x1= 1990
    • y1= 95
    • x2= 1999
    • y2= 221

    So the value of m is:

    m=\frac{221 - 95}{1999 - 1990}

    m=\frac{126}{9}

    m= 14

    So C(x)= 14*( x-1990) + b. In 1999, tuition had risen to $221 per credit hour. Replacing:

    221= 14*(1999 – 1990) + b

    221= 14*9 +b

    221= 126 + b

    221 – 126= b

    95= b

    Finally, the cost of tuition as a function of x, the number of years since 1990, is C(x)= 14*(x-1990) + 95

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