Question

1. a taxpayer claims the new sports team caused his school taxes to increase by 2%.

a. write an equation to show the relationship between the school taxes before and after a 2% increase. use b to represent the dollar amount of school tax before the 2% increase and t to represent the dollar amount of school tax after the 2% increase.
b. use your equation to complete the table below, listing at least 5 pairs of values.

b	t
1,000
2,000
	3,060
	6,120

Explanation:

Part (a)

Step1: Understand the percentage increase

A 2% increase means the new amount is the original amount plus 2% of the original amount. Mathematically, 2% of \( b \) is \( 0.02b \).

Step2: Form the equation

The tax after the increase (\( t \)) is the original tax (\( b \)) plus the increase (\( 0.02b \)). So, \( t = b + 0.02b \), which simplifies to \( t = 1.02b \) (since \( b + 0.02b=(1 + 0.02)b = 1.02b \)).

For \( b = 100 \):

Step1: Substitute \( b = 100 \) into \( t = 1.02b \)

\( t=1.02\times100 = 102 \)

For \( b = 1000 \):

Step1: Substitute \( b = 1000 \) into \( t = 1.02b \)

\( t = 1.02\times1000=1020 \)

For \( b = 2000 \):

Step1: Substitute \( b = 2000 \) into \( t = 1.02b \)

\( t=1.02\times2000 = 2040 \)

For \( t = 3060 \):

Step1: Use \( b=\frac{t}{1.02} \) (from \( t = 1.02b \), solve for \( b \))

\( b=\frac{3060}{1.02}=3000 \)

For \( t = 6120 \):

Step1: Use \( b=\frac{t}{1.02} \)

\( b=\frac{6120}{1.02} = 6000 \)

Answer:

\( t = 1.02b \)

Part (b)

We use the equation \( t = 1.02b \) (or \( b=\frac{t}{1.02} \) for finding \( b \) when \( t \) is known) to find the values.