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

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