Exponential and Logarithmic Functions: Part One — Test
Question 11 • Advanced Algebra: Concepts and Connections
A homeowner has an octagonal gazebo inside a circular area. Each vertex of the gazebo lies on the circumference of the circular area. The area that is inside the circle, but outside the gazebo, requires mulch. This area is represented by the function m times x , where x is the length of the radius of the circle in feet. The homeowner estimates that he will pay 1 point 5 0 dollars per square foot of mulch. This cost is represented by the function g of m , where m is the area requiring mulch. m times x is equal to pi x squared minus 2 square root of 2 x squared g of m is equal to 1 point 5 0 m Which expression represents the cost of the mulch based on the radius of the circle?
Answer
A
1 point 5 0 times open paren pi x squared minus 2 square root of 2 x squared close paren
B
1 point 5 0 times open paren pi times 1 point 5 0 x squared minus 2 square root of 2 1 point 5 0 x squared close paren
C
pi times 1 point 5 0 x squared minus 2 square root of 2 x squared
D
pi times 1 point 5 0 x squared minus 2 square root of 2 1 point 5 0 x squared
Explanation
The mulch area is m(x) = πx² − 2√2x². The cost is $1.50 per square foot, so substitute this area into g(m) = 1.50m: the cost is 1.50(πx² − 2√2x²). This matches choice D.
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