SOLUTION: John is doing a push-up challenge. On day one he does three pushups. Each day after the first John will do 10 push-ups per day. Write a function p(d) for the number of pushups John

Question 1143327: John is doing a push-up challenge. On day one he does three pushups. Each day after the first John will do 10 push-ups per day. Write a function p(d) for the number of pushups John will do on day d.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
on day 1, he does 3 pushups.
on every day after day 1, he does 10 pushups.
the general form of the linear equation for this is y = mx + b
when x = 1, y = 3
when x = 2, y = 13
the slope of the equation is equal to m which is equal to (13 - 3) / (2 - 1) = 10 / 1 = 10
the equation becomes y = 10x + b
to find the value of b, use one of the points on the line.
the point i used is the point equal to (1,3).
the equation becomes 3 = 10 * 1 + b
solve for b to get b = -7.
the equation becomes y = 10x - 7.
when x = 1, y = 3
when x = 2, y = 13
when x = 3, y = 23
the equation satisfies the requirements when x represents the number of days that the pushups are done.

you could also look at this as an arithmetic progression problem.
when viewed that way, you get
A1 = 3
An = 3 + (n-1) * d
d = 10
formula becomes An = 3 + (n-1) * d
when n = 1, A1 = 3 + 0 * 10 = 3
when n = 2, A2 = 3 + 1 * 10 = 13
when n = 3, A3 = 3 + 2 * 10 = 23
etc.

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