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) = . The function that gives the net points after the percentage increase in a player’s total points is s(p) = . Jack’s total score after winning the bonus points, given by the function (s ∘ b)(p), is . NextReset

Answer 1

The composition of the functions for receiving bonus points and the subsequent score increase results in the function (s ∘ b)(p) = (p + 10) × 1.05, which calculates Jack's total score after winning 3 consecutive games.

Step-by-step explanation:

The student's question pertains to the effects of consecutive wins on a player's score in a game. After winning 3 consecutive games, a player initially receives 10 bonus points. The player's score, denoted by s, then increases by 5% of their current points (p). The function that describes the addition of bonus points, b(p), would be b(p) = p + 10. To calculate the score after the percentage increase, the function s(p) can be represented as s(p) = p × 1.05. The composition of these functions, (s ∘ b)(p), which represents Jack's total score after winning the bonus points and then having his score increase by 5%, can be calculated by applying the percentage increase to the score with the bonus points, resulting in (s ∘ b)(p) = (p + 10) × 1.05.

Answer 2

The function can be described as

b(p)= player receives 10 bonus points
b(p)= p+10

s(p)= increases 5% of the player’s current points
s(p)= p*(100%+5%)= p*1.05

then (s ∘ b)(p) would be
s(p)= p*1.05
(s ∘ b)(p)= (p+10)*1.05
(s ∘ b)(p)= 1.05p+10.5