Question

If the federal government collects $1500 from every tax payer but spends $2500 on each tax payer every 12 months what is a function that would describe the amount of money earned by the government

Answer 1

The government loses $1000 per tax payer, according to the following function:

`y(x) = -1000*x`

Where "y" is the total money earned by the government and "x" is the number of tax payers.

Explanation:

Let's call the monetary balance of the government after one year "y", where "x" is the number of tax payers. Since each tax payer, "x", pays a total of $1500 every year, but the government spends $2500 with each one of them, then we can build a function "y(x)", with the value of collected tax being positive while the cost of each tax payer is negative, as shown below:

`y(x) = 1500*x - 2500*x\\y(x) = x*(1500 - 2500)\\y(x) = -1000*x`

The government loses $1000 per tax payer.