Question

Consider the function y = (0.92)". If t is measured in years, what is thepercent change in y every year?

Answer 1

Given:

$y=0.92^t$

To calculate percentage change,

At first year t=1,

$\begin{gathered} y_1=0.92^1 \\ y_1=0.92 \end{gathered}$

for second year t=2,

$\begin{gathered} y_2=0.92^2 \\ y_2=0.8464 \end{gathered}$

The percentage change is given by,

$\begin{gathered} P=\frac{y_2-y_1}{y_1}\times100 \\ =\frac{0.8464-0.92}{0.92}\times100 \\ =-8 \end{gathered}$

The percentage change in y is -8%