An exponential function is known to pass through and

MATHEMATICS · Subjective · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

An exponential function

g(x)=a^{x}

is known to pass through

(0,1)

and

(1,1.5)

. (a) Find the exact value of the base

a

. (b) Compute

g(3)

, leaving your answer correct to two decimal places. (c) Is the value obtained in part (b) greater than

4

or less than

4

? State your reasoning without solving any additional equations.