Question

The number of adults who attend a county fair (measured in hundreds of people) is represented by the function a(d)=−0.3d2+4d+9 , where d is the number of days since the fair opened. The number of children who attend the same county fair (measured in hundreds of people) is represented by the function c(d)=−0.2d2+5d+11 , where d is the number of days since the fair opened. What function, f(d) , can be used to determine how many more children than adults attend the fair on any day?

Answer 1

 f(d)=0.1d2+d+2 would be your answer I believe

Answer 2

Given is the function for number of adults who visit fair at day 'd' after its opening, a(d) = −0.3d² + 4d + 9.

Given is the function for number of children who visit fair at day 'd' after its opening, c(d) = −0.2d² + 5d + 11.  

Any function f(d) to find excess of children more than adults can be written as follows :-  

f(d) = c(d) - a(d).

⇒ f(d) = (−0.2d² + 5d + 11) - (−0.3d² + 4d + 9)

⇒ f(d) = -0.2d² + 0.3d² + 5d - 4d + 11 - 9

⇒ f(d) = 0.1d² + d + 2