I. Solve each item completely.

1. Shipping charges are often based on a formula that offers a lower charge per pound as the size of the shipment is increased. Suppose shipping charges are as follows: $2.20 per pound if the weight does not exceed 50 lb; $2.10 per pound if the weight is more than 50 lb but does not exceed 200 lb; $2.05 per pound if the weight is more than 200 lb.

a. Find a mathematical model expressing the total cost of a shipment as a function of its weight.

2. Due to the curvature of the earth, the maximum distance D that you can see from the top of a tall building or from an airplane at height h is given by the function

D(h)= √(2rh+h^2 )

where r =3960 mi is the radius of the earth and D and h are measured in miles.

a. How far can you see from the observation deck of Toronto’s CN Tower, 1135 ft above the ground?

b. Commercial aircraft fly at an altitude of about 7 mi. How far can the pilot see?

b. Commercial aircraft fly at an altitude of about 7 mi. How far can the pilot see?

3. A person’s approximate brain weight is directly proportional to his or her body weight, and a person weighing 150 lb has an approximate brain weight of 4lb.

a. Find a mathematical model expressing the approximate brain weight of a person as a function of the person’s body weight.

b. Find the approximate brain weight of a person whose body weight is 176 lb.

a. Find a mathematical model expressing the approximate brain weight of a person as a function of the person’s body weight.

b. Find the approximate brain weight of a person whose body weight is 176 lb.

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