Question

write an equation that expresses the output as a function of the input.
the total cost, c, after a sales tax of 7% is applied to the cost of a purchase, p.
determine the independent and dependent variables

Explanation:

Part 1: Writing the Equation

Step 1: Understand the tax application

The sales tax is 7% of the purchase cost \( p \). So the tax amount is \( 0.07p \) (since 7% = 0.07).

Step 2: Find the total cost

The total cost \( c \) is the purchase cost plus the tax. So \( c = p + 0.07p \).

Step 3: Simplify the equation

Combine like terms: \( p + 0.07p = 1.07p \), so \( c = 1.07p \).

The independent variable is the one that can be changed freely, which is the purchase cost \( p \) (we can choose different purchase amounts). The dependent variable depends on the independent variable; here, total cost \( c \) depends on \( p \) (as calculated by the equation).

Answer:

\( c = 1.07p \)

Part 2: Identifying Variables