Mathematics

Problem

Consider the functions

p(x)=4^{x}

and

q(x)=5\left(\dfrac12\right)^{x}

. Perform the following tasks. a. (i) Calculate the

y

–intercept of each function. b. (ii) Sketch the graphs of

p

and

q

on the same pair of axes, indicating the intercepts and horizontal asymptotes. c. (iii) From your sketch, estimate the value of

x

at which

p(x)=q(x)

. d. (iv) Hence state the set of real numbers

x

for which

p(x)>q(x)

, explaining how the sketch supports your answer.