Acharity organization had a fundraiser where each ticket was sold for a fixed price. they had to sell a few tickets just to cover necessary production costs of $1200\$1200 $1200 dollar sign, 1200 . after selling 200200 200 200 tickets, they had a net profit of $12,000\$12{,}000 $12,000 dollar sign, 12, comma, 000 . let p(n)p(n) p(n) p, left parenthesis, n, right parenthesis denote the net profit from the fundraiser pp p p (measured in dollars) as a function of the number of tickets sold nn n n . write the function's formula

Step-by-step explanation:

Let x be the revenue collected from selling each ticket.

We have been given that a charity organisation had to sell a few tickets just to cover necessary production costs of $1200. After selling 200 tickets, they had a net profit of $12,000.

Since we know that net profit is the difference between total revenue and total cost.

We can represent our given information in an equation to find the revenue collected from each ticket:

Let us solve for x by adding 1200 to both sides of equation.

Therefore, the revenue collected from selling each ticket is $66.

Now let us write the net profit, P(n), from fundraiser as the function of number of tickets sold,n.

The revenue from selling n tickets will be 66n.

Production costs = 1200

Therefore, our desired function will be: .

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt

is there a graph

step-by-step explanation: