# How to Use Growth Factors in Calculations

You use growth factor in the formula below, and solve the calculation or equation that appears. When using the formula, you always insert $x$ for the value you want to find.

Formula

### Calculationofnewvalue,oldvalueandgrowthfactor

New value = old value $\cdot$ growth factor

Example 1

The price of a car decreases by $5$ %. What will the price be after the decrease if the price of the car is $$20\phantom{\rule{0.17em}{0ex}}000$? Here the old price is$$20\phantom{\rule{0.17em}{0ex}}000$, new value $=x$, and the growth factor is as follows:

 $\phantom{\rule{-0.17em}{0ex}}\left(1-\frac{5}{100}\right)=1-0.05=0.95$

The new price will be

Example 2

iPhone 13 costs $$799$ and is increased by $15$ % from iPhone 12. What did the iPhone 12 cost? Here is old price $=x$, new value$$799$, and the growth factor becomes

 $\phantom{\rule{-0.17em}{0ex}}\left(1+\frac{15}{100}\right)=1+0.15=1.15$

The old price was thus:

So, an iPhone 12 costs $$694.78$. Example 3 An item originally costed$$599$. The price was reduced to \$$349$, and the store says that the item is lowered by $45$ %. Is it true?

To find $p$, you must first find the growth factor. You do this by using the formula above.

Let’s call the growth factor gf to save some space.

Since the value of the growth factor is less than $1$, you get confirmed that it is a drop in price. Then you use the formula for growth factor, with minus, to find $p$ in percentage: $\begin{array}{llll}\hfill 0.583& =1˘\frac{p}{100}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill \frac{p}{100}& =1˘0.583\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill \frac{p}{100}& =0.417\phantom{\rule{2em}{0ex}}|\cdot 100\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill p& =41.7\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

The price has only been reduced by $41.7$ %. You could have been tricked!