A function of the form has and it also passes through the point .

MATHEMATICS · Multi-part · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

A function of the form

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

has

f(0)=3

and it also passes through the point

(4,48)

. (i) Find the values of

a

and

b

. (ii) State whether the function represents exponential growth or exponential decay, giving a brief reason. (iii) Using the values of

a

and

b

obtained in part (i), calculate

f(-2)