Consider two functions of time t:
f(t) = 0.01t^2
g(t) = 4t
where 0

Question

Consider two functions of time t: f(t) = 0.01t^2 g(t) = 4t where 0 < t < infinity. Now consider the following two statements: i. For some t > 0, g(t) > f(t). ii. There exists a T such that f(t) > g(t) for all t > T. Which one of the following options is TRUE? A. only (i) is correct B. only (ii) is correct C. both (i) and (ii) are correct D. neither (i) nor (ii) is correct

Accepted Answer

Both statements are correct; answer is C We have a quadratic function f(t) = 0.01t^2 and a linear function g(t) = 4t, both for positive t. The quadratic eventually dominates the linear (since degree 2 grows faster than degree 1), but for small t the linear part is larger. Statement (i) asks whether g ever exceeds f — it does, for small t near the origin. Statement (ii) asks whether f eventually stays permanently larger than g — it does, after the second intersection point.