Question

Find the multiplier for each rate of exponential growth or decay.

1. 1% growth
2. 7% decay
3. 1% decay

Answer 1

Answer:

1. 1.01

2. 0.93

3. 0.99

Step-by-step explanation:

The exponential function which models the exponential growth has a form

$y=C(1+r)^x,$

where C is initial amount, y is final amount, x is time, r is rate (the percent written as a decimal) and 1+r is a multiplier.

The exponential function which models the exponential decay has a form

$y=C(1-r)^x,$

where C is initial amount, y is final amount, x is time, r is rate (the percent written as a decimal) and 1-r is a multiplier.

Thus,

1. 1% growth has a multiplier 1+0.01=1.01;

2. 7% decay has a multiplier 1-0.07=0.93;

3. 1% decay has a multiplier 1-0.01=0.99.