A study prepared for the National Association of Realtors estimated that the number of housing starts per year over the next 5 years will be N(r) =
7
1 + 0.02r 2
million units, where r (percent) is the mortgage rate. Suppose the mortgage rate t months from now will be
r(t) =
5t + 75
t + 10
(0 ≤ t ≤ 24)
percent/year.
(a) Find an expression for the number of housing starts per year as a function of t, t months from now.

that there are 12 data points

step-by-step explanation:

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step-by-step explanation:

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let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: