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scZoUnD [109]
2 years ago
9

+

Mathematics
1 answer:
nikdorinn [45]2 years ago
6 0

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

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