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)

the answer   is 200

step-by-step explanation:

this is a problem about poisson probabilities.   i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.  

here's how you can see a poisson distribution coming.   when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution.   this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot.   there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything.   the form of the distribution is

  probability of n chips = {[e^(-x)]*(x^n)} / (n! )

add all the numbers and check the ones place.

the answer is 486. as the ones place is more than 4, the estimation will be the next 10 ie, 490