(a) Use a graphing utility to approximate the integrals of the functions and on the

Chapter 5, Problem 113

(choose chapter or problem)

Conjecture

(a) Use a graphing utility to approximate the integrals of the functions

\(f(t)=4\left(\frac{3}{8}\right)^{2 t / 3}, g(t)=4\left(\frac{\sqrt[3]{9}}{4}\right)^{t}\), and \(h(t)=4 e^{-0.653886 t}\)

on the interval [0, 4].

(b) Use a graphing utility to graph the three functions.

(c) Use the results of parts (a) and (b) to make a conjecture about the three functions. Could you make the conjecture using only part (a)? Explain. Prove your conjecture analytically.

Text Transcription:

f(t) = 4(3/8)^2t/3, g(t) = 4(cube root 9/4_^t

h(t) = 4e^-0.653886t