Question

Jack is playing a game. When a player wins 3 consecutive games, the player receives 10 bonus points and then the player’s total score, s, increases by 5% of the player’s current points. Jack currently has p points and has won 3 consecutive games.

The function that represents a player’s points including the bonus points, b , is 

b(p ) = (blank)

The function that gives the net points after the percentage increase in a player’s total points is s(p ) = (blank)

Jack’s total score after winning the bonus points, given by the function (s  ∘  b)(p ), is(blank)

Answer 1

Let Jack's current point is
`p`

After winning 3 consecutive games, the bonus point is given by

`b(p)=p+10`

The score after 5% = 0.05 increase is

`s(p)= (1+0.05)p=1.05p`


`(s.b)(p)=1.05(p+10)=1.05p+10.5`