Consider the function

MATHEMATICS · Multi-part · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

q(x)=k\cdot5^{x}

, where

k\neq0

is a constant. (i) Verify that

q(0)=k

. (ii) If

q(3)=40

, determine the value of

k

. (iii) Using the value of

k

found in part (ii), calculate

q(-1)

and

q(2)

. (iv) Hence find the percentage increase from

q(-1)

q(2)

, correct to two decimal places. (v) Show that for any integers

m>n

, the quotient

\dfrac{q(m)}{q(n)}

equals

5^{\,m-n}