Question

Need help with these 3 questions please explain how you do It. Thx!

Answer 1

1. Observe that the f(t) is change by 4 per time t => there's a acceleration of 4 => f''(t) = 4;  Take the derivative of it we can get a velocity function. f'(t) = 4t + c. Since the velocity from 100 to 80 is -20 (average), this means at t = 0, f'(0) = -22 => f'(t) = 4t - 22; Take the derivative again to get the position function: f(t) = 2t^2 - 22t + d, here d = 100 should be trivial. So, the function that models the relationship is    f(t) = 2t^2 - 22t + 100.

2. By the compound interest formula:
    A = P (1 + r/n)^(nt) , since it's yearly, so n = 1;
    results A(t) = 100 (1+0.12)^t.

3. The average rate of change is basically finding the slope, m = y1 - y2 / x1 - x2.