Directions: Answer each question, show your work in full detail, and clearly sta

Question

Directions: Answer each question, show your work in full detail, and clearly state your final answer. Explanations should be given in complete sentences. Graphs (if required) should be fully labeled. Proper notation and units (where applicable) are required Problem 1: (15 points) A shop has determined that the number of bottles of water they sell on a summer day is a function of the day's high temperature, given by N(T) = 5T+12 The variable T is the day's high temperature and 80 sT 110. Suppose that the predicted high temperatures for the next 7 days are given in the table below Day: t (days High Temp: 1 23 4 959697 98 99 100 101 egrees Express the high temperature as a function T(t) of the day. Use this function to create another function N(t) that represents the number of bottles of water sold as a function of the day. What is the domain of this function Pick one ordered pair on the graph of N(t) and explain what it tells you in practical terms

Explanation / Answer

1. It can be observed that the high temperature increases by 1 unit each day.

T(t) = 94 + t

N(T) = 5T + 12

N(t) = 5(94 + t) + 12

= 470 + 5t + 12

= 5t + 482

80 < T < 110

412 < N(T) < 562

412 < 5t + 482 < 562

-60 < 5t < 80

-12 < t < 16

Since t> 0

Domain of N(t) is (0, 16]

Number of bottles sold increases linearly wrt number of days.

2. A(d) and T(d) intersect at 7/25

Hence (T - A)(d) is positive before 7/25, i.e. 7/17 to 7/25

(T-A)(d) is zero on 7/25

(T - A)(d) is negative after 7/25

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