Mathematics

Problem

Consider an exponential function that passes through the points

(1,6)

and

(-2,0.96)

. a. (i) Determine the values of

a

and

b

f(x)=a\,b^{x}

. b. (ii) Decide, with justification, whether the function is increasing or decreasing on

\mathbb{R}

. c. (iii) Sketch a rough graph of the function on the same set of axes, clearly marking the

y

-intercept and the two given points.