A car dealership is offering 1 dollars comma 500 cash back on the purchase of a new vehicle. The cost, after the cash back, of a new vehicle can be modeled by the function cap c times x is equal to x minus 1 comma 500 , where x is the original price of the vehicle. The vehicle is subject to a sales tax of 8 point 4 3 percent , so the total price of the vehicle is represented by the function cap p times cap c is equal to 1 point 0 8 4 3 cap c Which function can be used to represent the final price of the vehicle based on the original price, after the discount and tax have been applied?
Answer
A
cap p times open paren cap c times x close paren is equal to 1 point 0 8 4 3 x minus 1 comma 500
B
cap p times open paren cap c times x close paren is equal to 1 point 0 8 4 3 x minus 1 comma 626 point 4 5
C
cap c times open paren cap p times x close paren is equal to 1 point 0 8 4 3 x minus 1 comma 500
D
cap c times open paren cap p times x close paren is equal to 1 point 0 8 4 3 x minus 1 comma 626 point 4 5
Explanation
First apply the $1,500 cash-back discount: c(x) = x − 1,500. Then apply the 8.43% sales tax by multiplying the discounted price by 1.0843: p(c(x)) = 1.0843(x − 1,500) = 1.0843x − 1,626.45. Choice B gives this function; the discount is also taxed, so the constant term is not just $1,500.
AI-written and checked against the verified answer.