Suppose a tortoise is 2000 feet from the ocean. Each day the tortolse travels on

Question

Suppose a tortoise is 2000 feet from the ocean. Each day the tortolse travels one-half of the remaining distance to the ocean. Use this information to: a. Construct a model that represents the remaining distance that the tortoise must travel to reach L,00, (t) the ocean. b. Compute the remaining distance to the ocean after 4 days of travel. A certain vehicle loses 35% of its value each year. If the vehicle has an initial value of $25,000, construct a model that represents the value after x years. a. b. Compute the value of the vehicle at the end of the 3'd year Atmospheric pressure decreases by about 12% for every 1000 meters you climb. The pressure at sea level is about 1013 atmospheres a. Construct a model to represent the atmospheric pressure at a given altitude in thousands of meters. 1,ooometers 12 lb b. How many atmospheres of pressure will you feel at 5,895meters? (Top of Mt. Kilimanjaro) c. How many atmospheres of pressure will you feel at 8,848 meters? (Top of Mt. Everest) d. How many atmospheres of pressure will you feel at 383 meters? (highest point in Indiana)

Explanation / Answer

Question 1 : The torotoise model.

S(t) = 2000 * (1/2)t

Where S(T) is the distance remaining and t = time

(b) t = 4 days

S(t) = 2000 * (1/2)4 = 125m

Question 2 Vehicle depreciation

D(t) = 25000 * (1 - 0.35)t  = 25000 * (0.65)t

D(t) = 25000 * (0.65)t

(b) t = 3 years

D(3) = 25000 * (0.65)3 = $ 6865.625

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