The following graph shows the average annual college tuition costs (tuition and
ID: 2871698 • Letter: T
Question
The following graph shows the average annual college tuition costs (tuition and fees) for a year at a private nonprofit or public four-year college. The data are given for five-year intervals.
The tuition for a private college is approximated by the function
f(x) = 650x2 + 3000x +12,000,
where x is the number of five-year intervals since the academic year 1995-96 (so the years in the graph are numbered
x = 0
through
x = 3).
(a) Use this function to predict tuition in the academic year 2020-21. [Hint: What x-value corresponds to that year?]
$
(b) Find the derivative of this function for the x-value that you used in part (a).
$
Interpret it as a rate of change in the proper units.
In 2020-2021, private college tuition will be ---Select--- increasing decreasing by $ every 5 years.
(c) From your answer to part (b), estimate how rapidly tuition will be increasing per year in 2020-21.
$
Explanation / Answer
f(x) = 650x2 + 3000x +12,000
(a) Use this function to predict tuition in the academic year 2020-21. [Hint: What x-value corresponds to that year?]
$ x=5
f(5) = 650*52 + 3000*5 +12,000 =43250$
(b) Find the derivative of this function for the x-value that you used in part (a).
$
f(x) = 650x2 + 3000x +12,000
f'(x) = 2*650x + 3000*1 +0
f'(x) = 1300x + 3000 dollars per year
increasing
(c) From your answer to part (b), estimate how rapidly tuition will be increasing per year in 2020-21.
f'(5) = 1300*5 + 3000 =9500dollars per year
$
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