Answer:
The function f(t) = 0.0037(t + 14.979)^2 can be rewritten as f(t) = 0.0037(t^2 + 29.958t + 222.126). This is a quadratic function that has been stretched vertically by a factor of 0.0037 and shifted 14.979 units to the right and 222.126 units up.
To sketch the graph of this function, we can start with the graph of f(t) = t^2, which is a parabola that opens upwards. The transformation of this function stretches the parabola vertically by a factor of 0.0037, so its maximum and minimum values will be much smaller. The shift of 14.979 units to the right means that the vertex of the parabola will be located 14.979 units to the right of the vertex of the original parabola. The shift of 222.126 units up means that the minimum value of the function will be located 222.126 units above the minimum value of the original parabola.
On the interval 0 ≤ t ≤ 19, the graph of the function will be a parabola that stretches vertically by a factor of 0.0037 and is shifted 14.979 units to the right and 222.126 units up from the graph of f(t) = t^2.
To predict the mortgage debt in the year 2014, we can substitute t = 24 into the function f(t) = 0.0037(t + 14.979)^2. This gives us f(24) = 0.0037(24 + 14.979)^2 = 0.0037(39.979)^2 = 0.0037 * 1595.7441 = 5.90834 trillion dollars. This is the predicted mortgage debt in the year 2014.