Mathematics

Problem

The graph of an exponential function passes through the points

(1,6.25)

and

(3,156.25)

. a. (i) Determine the equation of the function in the form

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

. b. (ii) Using the equation obtained, compute the value of

f(-1)

. c. (iii) Comment on how your answer in part (ii) relates to the fact that the

x

-axis is a horizontal asymptote of any exponential function.