# A certain country taxes the first $19,000 of an individual&39;s income at a rate of 15%, and all income over$19,000 is taxed at 25%. How do you find a piecewise-defined function T that specifies the total tax on an income of x dollars?

Feb 12, 2018

See a solution process below:

#### Explanation:

First, let's call the individual's income: $i$

Let's call the amount of tax they will pay: $t$

"Percent" or "%" means "out of 100" or "per 100",

Therefore, 15% can be written as $\frac{15}{100}$.

And, 25% can be written as $\frac{25}{100}$.

Then if, the individuals income is less than or equal to $19,000 the amount of tax they will pay in terms of $i$is: $t = \frac{15}{100} i$$t = \frac{3}{20} i$The amount of tax they will pay if they earn more than$19,000 is:

t = (15/100 xx $19000) + 25/100(i -$19000))

t = $2850 + 25/100(i -$19000))

t = $2850 + 25/100i -$4750

t = 25/100i - $1900 t = 1/4i -$1900

The piece wise function would be:

y = {3/20i" for "i <= $19000; color(white)("..........")1/4i -$1900 " for "i > \$19000}#