# Last year the income for a business was 2,000,000. This year the income grew 15%. What was the income for the business this year?

Dec 28, 2016

The income in 2010 is 2.3 million

#### Explanation:

The formula for determining rate of change over time is:

$\frac{p}{100} = \frac{N - O}{O}$

Where $p$ is the percentage change (for this problem $15$)

Where $O$ is the old value (for this problem $2000000$

Where $N$ is the new value (what we are solving for in this problem)

Substituting and solving for $N$:

$\frac{15}{100} = \frac{N - 2000000}{2000000}$

$\frac{15}{100} = \frac{N}{2000000} - \frac{2000000}{2000000}$

$\frac{15}{100} = \frac{N}{2000000} - 1$

$\frac{15}{100} + \textcolor{red}{1} = \frac{N}{2000000} - 1 + \textcolor{red}{1}$

$\frac{15}{100} + \left(\textcolor{red}{1} \cdot \textcolor{b l u e}{\frac{100}{100}}\right) = \frac{N}{2000000} - 0$

$\frac{15}{100} + \frac{100}{100} = \frac{N}{2000000}$

$\frac{115}{100} = \frac{n}{2000000}$

$\textcolor{red}{2000000} \cdot \frac{115}{100} = \textcolor{red}{2000000} \cdot \frac{N}{2000000}$

$\frac{230000000}{100} = \cancel{\textcolor{red}{2000000}} \cdot \frac{N}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2000000}}}}$

$2 , 300 , 000 = N$