Question

millage rate is the amount per $1000 that is often used to calculate property tax. for example, a home with a $60,000 taxable value in a municipality with a 16 mill tax rate would require (0.016)($60,000) = $960 in property taxes. in one county, homeowners pay a flat tax of $190 plus a rate of 16 mill on the taxable value of a home.
part 1 of 2
(a) write a linear function that represents the total property tax ( t(x) ) for a home with a taxable value of ( x ) dollars. the linear function is ( t(x) = square ) for ( x geq 0 ).
part 2 of 2
(b) evaluate ( t(50,000) ) and interpret the meaning in the context of this problem. ( t(50,000) = square ) means that the property tax is $ square $ for a home with a taxable value of $ square $.

Explanation:

Step1: Define linear tax function

A linear function has the form $T(x) = mx + b$, where $b$ is the flat tax, and $m$ is the mil tax rate converted to a decimal. A 16 mil rate means $\frac{16}{1000} = 0.016$, and the flat tax is $190$.
$T(x) = 0.016x + 190$ for $x\geq0$

Step2: Substitute $x=50000$ into $T(x)$

Calculate the tax by plugging $x=50000$ into the function.
$T(50000) = 0.016(50000) + 190$

Step3: Compute the tax amount

First calculate the mil tax portion, then add the flat tax.
$0.016(50000) = 800$; $800 + 190 = 990$

Answer:

(a) $T(x)=0.016x + 190$
(b) $T(50,000)=990$ means that the property tax is $\$990$ for a home with a taxable value of $\$50,000$.