How to Use Growth Factors in Calculations

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Encyclopedia>Numbers and Quantities>Fractions and Percentages>Percentages>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

Calculation of new value, old value and growth factor

New value = old value $\cdot$ growth factor

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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 $ $20 000$ ?

Here the old price is $ $20 000$ , new value $= x$ , and the growth factor is as follows:

(1 - \frac{5}{100}) = 1 - 0.05 = 0.95

The new price will be

\begin{array}{l} new value & = old value \cdot growth factor \\ x = $ 20 000 & \cdot 0.95 = $ 19 000 \end{array}

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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

(1 + \frac{15}{100}) = 1 + 0.15 = 1.15

The old price was thus:

\begin{array}{l} new value & = old value \cdot growth factor \\ 799 & = x \cdot 1.15 \\ \frac{799}{1.15} & = \frac{x \cdot 1.15}{1.15} \\ x & \approx 694.78 \end{array}

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.

\begin{array}{l} new value & = old value \cdot gf \\ 349 & = 599 \cdot gf | : 599 \\ gf & = \frac{349}{599} \approx 0.583 \end{array}

\begin{array}{l} new value & = old value \cdot growth factor \\ 349 & = 599 \cdot growth factor | : 599 \\ growth factor & = \frac{349}{599} \approx 0.583 \end{array}

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}{l} 0.583 & = 1 - \frac{p}{100} \\ \frac{p}{100} & = 1 - 0.583 \\ \frac{p}{100} & = 0.417 | \cdot 100 \\ p & = 41.7 \end{array}

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

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