An exponential curve passes through the points and

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

Problem

An exponential curve passes through the points

(0,5)

and

(1,8)

. The

x

-axis is its horizontal asymptote. (i) Find the value of the base

b

of the function if it is written in the form

f(x)=5 b^{x}

. (ii) Hence, write the equation of the function.