Simba Travel Agency arranges trips for climbing Mount Kilimanjaro. For each trip, they charge an initial fee of $100 dollars, in addition to a constant fee for each vertical meter climbed. For instance, the price for climbing to the Shira Volcanic Cone, which is 3000 meters above the base of the mountain, is $400 dollars. Let F (d) denote the fee of a trip F (measured in dollars) as a function of the vertical distance climbed d (measured in meters). Write the function's formula.

Question

Carolyn Torres

Mathematics

10 March, 05:01

Simba Travel Agency arranges trips for climbing Mount Kilimanjaro. For each trip, they charge an initial fee of $100 dollars, in addition to a constant fee for each vertical meter climbed. For instance, the price for climbing to the Shira Volcanic Cone, which is 3000 meters above the base of the mountain, is $400 dollars. Let F (d) denote the fee of a trip F (measured in dollars) as a function of the vertical distance climbed d (measured in meters). Write the function's formula.

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Answers (1)

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Erickson · Answer 1

The formula is F (d) = 100+0.10d.

We must find the cost per meter to write the function. We know that the cost to climb a 3000 meter mountain was 400:

400=100+3000 (x)

Subtract 100 from each side:

400-100 = 100+3000x-100

300 = 3000x

Divide both sides by 3000:

300/3000 = 3000x/3000

0.10 = x

This is the cost per meter. Using this, we have the formula

F (d) = 100+0.10 (d)