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Suppose a tortoise is 1000 feet from the ocean. Each day the tortoise travels three-fifths of theremaining distance to the ocean. Use this information to:16. Construct a model that represents the remaining distance that the tortoise must travel to reach the ocean.17. Compute the remaining distance to the ocean after 4 days of travel.

User Ben Voigt
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1 Answer

8 votes
8 votes

Since the tortoise travels 3/5 the remaining distance, the remaining distance at the end of the day is:

5/5 - 3/5 = 2/5

2/5 of what it was at the beginning of the day.

So, the function can be modeled by an exponential with a "growth" factor of 2/5, as follows:

r(n) = 1000 × (2/5)ⁿ

where, r is the number of remaining feet after n days of travel.

To find the remaining distance after 4 days of travel:

r(4) = 1000 × (2/5)⁴

r(4) = 25.6 ft

User Tylerjroach
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