Question

The number of adults at an amusement park, measured in hundreds of people, is represented by the function a(w)=−0.4w^2+5w+9, where w is the number of weeks since the amusement park opened for the season.

The number of children at the same amusement park, measured in hundreds of people, is represented by the function c(w)=−0.2w^2+9w+12, where w is the number of weeks since the amusement park opened for the season.

What function, f(w) , can be used to determine how many more children than adults are at the amusement park any week during the season?

Answer 1

0.2w^2+4w+3

Explanation:

a(w)=−0.4w^2+5w+9

c(w)=−0.2w^2+9w+12

We want to find the how many more children than adults

f(w) = c(w) - a(w)

= −0.2w^2+9w+12 - ( −0.4w^2+5w+9)

Distribute the minus sign

= −0.2w^2+9w+12 +0.4w^2-5w-9

Combine like terms

= 0.2w^2+4w+3