A modern art piece includes drops of paint spilling periodically into a basin of liquid. The display is timed with an expectation that the circular area of the green spill increases 1 point 5 square centimeter per hour. Increase in area: cap A times h is equal to 1 point 5 h ; h in hours Increase in diameter: d times cap A is equal to square root of cap A over pi end root ; cap A in square centimeters The artist would like to know the area of the spill after any number of hours, h Which composite function represents the diameter of the green paint as a function of hours?
Answer
A
d times open paren cap A times h close paren is equal to 2 square root of 1 point 5 h over pi end root
B
d times open paren cap A times h close paren is equal to 2 square root of 1 point 5 cap A over pi end root
C
d times open paren cap A times h close paren is equal to 3 square root of h over pi end root
D
d times open paren cap A times h close paren is equal to 3 square root of cap A over pi end root
Explanation
The area after h hours is A(h) = 1.5h square centimeters. The diameter of a circular spill with area A is d(A) = 2√(A/π), since the radius is √(A/π) and the diameter is twice the radius. Substituting A(h) into the diameter formula gives d(A(h)) = 2√(1.5h/π), which is choice A.
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