Answer:
1 n) = -2n^2 + 2
2 Let x be the number of chocolate hearts sold. The number of rose bouquets sold is x + 15. The total cost of the chocolate hearts is 3x and the total cost of the rose bouquets is 5(x + 15). The total cost of both products is 3x + 5(x + 15) = 3x + 5x + 75 = 8x + 75 = $339. Solving this equation for x, we get x = (339 - 75) / 8 = 64. So the number of chocolate hearts sold is 64.
3 The price of the ticket is increasing at a constant rate. This suggests that the price of the ticket is following an arithmetic sequence. The formula for the nth term of an arithmetic sequence is t(n) = a + (n-1)d, where a is the first term, d is the common difference, and n is the number of terms.
Using the given information, we can find the common difference, d = t(2) - t(1) = $60.50 - $55 = $5.50.
Now, to find the price of the ticket after 6 years, we can use the formula t(n) = a + (n-1)d where n = 6, a = $50, and d = $5.50.
So t(6) = $50 + (6-1)$5.50 = $50 + 5$5.50 = $50 + $27.50 = $77.50. So, the price of the ticket in 6 years will be $77.50.