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

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

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

(b) Determine the tax due if the tax rate increases 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%?

Transcribed Image Text:

T = f(r, v, x) = r 100 -(.40v - x),