Question

What is the growth factor associated with the following growth rate: 30% decrease

Answer 1

Given:

Growth rate = 30% decrease

To find:

The growth factor associated with the given growth rate.

Solution:

The general exponential function is:

$y=a(1+r)^x$

$y=a(b)^x$

Where, a is the initial value, r is the growth rate in decimal and $b=1+r$ is the growth factor.

It is given that the growth rate is 30% decrease. So,

$r=-30\%$

$r=-\dfrac{30}{100}$

$r=-0.3$

Now,

$b=1+r$

$b=1+(-0.3)$

$b=1-0.3$

$b=0.7$

Therefore, the growth factor is 0.7.