Question

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y = 3900(0.937)

Answer 1

ANSWER

This function represents a decay. The rate of decrease is 6.3%

EXPLANATION

When the growth/decay factor is less than 1, the function represents a decay:

$y=a(b)^x$

b is the growth/decay factor.

For a function that represents decay, the decrease factor is:

$b=1-r$

where r is the rate of decrease. In this case, b = 0.937. We can find r:

$\begin{gathered} 0.937=1-r \\ r=1-0.937 \\ r=0.063 \end{gathered}$

To know the rate as a percentage, we have to multiply it by 100:

$r=0.063\times100=6.3\text{ \%}$