Question

The number of pairs of shoes increases and decreases by the function s(t)=-2|t—15|+50, where is the time (in weeks) what is the function and what is the greatest number of Paris of shoes sold in one week?

Answer 1

The function is s(t) = -2|t - 15| + 50, where t represents the time in weeks. The greatest number of pairs of shoes sold in one week is 2t + 20.

Step-by-step explanation:

The given function is s(t) = -2|t - 15| + 50, where t represents the time in weeks.

To find the greatest number of pairs of shoes sold in one week, we need to find the maximum value of the function. The function is a piecewise function with two parts:

1. When t < 15: s(t) = -2(t - 15) + 50
2. When t ≥ 15: s(t) = -2(-(t - 15)) + 50

Let's evaluate both cases:

1. When t < 15: s(t) = -2(t - 15) + 50 = -2t + 30 + 50 = -2t + 80
2. When t ≥ 15: s(t) = -2(-(t - 15)) + 50 = 2t - 30 + 50 = 2t + 20

The greatest number of pairs of shoes sold in one week will occur when the function reaches its maximum value. Since the coefficient of t in the second case is positive (2t + 20), this case will have a greater value than the first case (-2t + 80). So, to find the maximum value, we need to evaluate s(t) when t ≥ 15:

s(t) = 2t + 20

Therefore, the greatest number of pairs of shoes sold in one week is 2t + 20.