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.

Accepted Solution

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:

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.Β  Using this, we have the formula
F(d) = 100+0.10(d)