Chapter 7.1, Problem 13E

Tax and Homeowner Exemption The value of residential property for tax purposes is usually much lower than its actual market value. If $v$ is the market value, the assessed value for real estate taxes might be only $40\%$ of $v$. Suppose that the property tax, $T$, in a community is given by the function

$T=f\left(r,v,x\right)=\frac{r}{100}\left(0.40v-x\right)$,

Where $v$ is the market value of the property(in dollars), $x$ is a homeowner’s exemption (a number of dollars depending on the type of the property), and $r$ is the tax rate (stated in dollars per hundred dollars).

Determine the real estate tax on a property valued at $\$200,000$ with a homeowner’s exemption of $\$5000$, assuming atax rate of $\$2.50$ per hundred dollars of net assessed value.

Determine the tax due if the rate increased by $20\%$ to $\$3.00$ per hundred dollars of net assessed value. Assume the same property value and homeowner’s exemption. Does the tax due also increase by $20\%?$