Mathematics

Problem

The graph of an exponential function has the horizontal asymptote

y=3

and passes through the points

P(2,4)

and

Q(3,10)

. (i) Show that the equation of the function can be expressed in the form

y=3+b^{x-k}

. Hence determine the values of

b

and

k

. (ii) Using the equation obtained, find the

y

-intercept of the graph. (iii) State, with justification, whether the function is increasing or decreasing on its domain.