Answer:
[tex]f(n)=-0.10n^2+8n+200[/tex]
Step-by-step explanation:
Let n represent number of new members and f(n) represent membership money.
We have been given that there are currently 20 members in the school's Ski Club. So when n new members join, the total number of members would be [tex]20+n[/tex].
Since for each new member recruited the dues for all members will be reduced by 10 cents, so new dues would be [tex]10-0.10n[/tex].
The membership money would be number of total members times dues as:
[tex]f(n)=(20+n)(10-0.10n)[/tex]
Since we need our equation in standard form, so we will use FOIL to expand our equation as:
[tex]f(n)=20(10)-20(0.10n)+n(10)-n(0.10n)[/tex]
[tex]f(n)=200-2n+10n-0.10n^2[/tex]
[tex]f(n)=200+8n-0.10n^2[/tex]
[tex]f(n)=-0.10n^2+8n+200[/tex]
Therefore, our required equation would be [tex]f(n)=-0.10n^2+8n+200[/tex].
