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All courses Math I · F-LE.1.c 30 of 59
Recognize constant percent growth or decay as evidence for an exponential model.

Convert percent increase to growth factor

Problem
Identify the growth factor for a constant percent increase of 5%.
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Hint

Rewrite 5% as the decimal 0.05. For growth, add the decimal increase to 1.

A growth factor keeps the original whole and adds the increase. So a 5% increase means 1 + 0.05 = 1.05.

Solution walkthrough

01

Convert the percent increase

\[5\%=5/100=0.05\]

The decimal 0.05 represents the added portion of the original amount.

02

Keep the original whole

\[\text{growth}~\text{factor}=1+0.05\]

A percent increase retains all of the original amount, represented by 1, and adds the decimal increase.

03

Calculate the multiplier

\[1+0.05=1.05\]

The factor 1.05 means the new value is 105% of the previous value: 100% retained plus 5% added.

04

State and check the factor

\[1.05\]

For example, 100(1.05)=105, exactly a 5% increase from 100.

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Another way

  1. Compute the retained percentage directly: 100%+5%=105%=1.05.

!

Common mistake

Do not use 0.05 alone. That represents only the increase, not the original amount plus the increase.