The give quadratic function is dilated by the given coefficient, and shifted
horizontally to the left.
(a) The transformation of the common function f(x) are;
- f(t) is made more wider than f(x)
- f(t) is shifted more to the left than the common function f(x).
Please find attached the required graph created with MS Excel
(b) Where t = 0, represent the year 2,000 we have;
- <u>f(t) = 0.0037·(t + 24.979)²</u>
(c) The mortgage debt in the year 2014 is M ≈ <u>$5.622 trillion</u>
Reasons:
The given function is f(t) = 0.0037·(t + 14.979)²
Year 1990 is t = 0
(a) The given common function is; f(x) = x²
The transformation of the quadratic function are;
The coefficient 0.0037 widens the common function such that f(t) is wider
than f(x).
The constant, 14.979 added to the variable, <em>t</em>, shifts the graph of the
common function horizontally to the left.
Therefore;
- <u>f(t) is wider and shifted to the left more than the common function f(x)</u>
Please find attached the required graph over the interval 0 ≤ t ≤ 19 created with MS Excel.
(b) The amount of mortgage debt in 2,000 is given as follows;
With t' = 0 represent the year 2,000, we have;
At year 1990, t' = -10
Which gives, t' = t + 10
From which we have;
f(t) = 0.0037·(t + 14.979)² = 0.0037·(t' + 10 + 14.979)² = 0.0037·(t' + 24.979)²
Therefore;
The function with t = 0 representing the year 2,000 is presented as follows;
<u>f(t) = 0.0037·(t + 24.979)²</u>
(c) In the year 2014, we have;
t = 2014 - 2000 = 14
Which gives;
f(14) = 0.0037·(14 + 24.979)² ≈ 5.622
The mortgage debt in the year 2014 is M ≈ <u>$5.622 trillion dollars</u>
Learn more about transformation of quadratic functions here:
brainly.com/question/15105480
