Question

Oil is leaking from a damaged shipping vessel stranded at sea.

The captain estimates that the costs, C, in millions of dollars, to clean a t ton oil spill can be modeled by the function C(t)=1.5t+2,
The amount of oil, S, in tons, that has been spilled in d days is given by the function S(d)=355d.
Find an explicit expression that models the costs of cleaning up a d day oil spill.

Answer 1

The explicit formula that will be used to find the cost of cleaning up d day oil spill is:

`CoS(d)=532.5d+2`

Explanation:

The amount of oil, S, in tons, that has been spilled in d days is given by the function:

S(d)=355d.

The cost to clean a t ton oil spill can be modeled by the function:

C(t)=1.5t+2

This means that the cost to clean in d days is given by the composition function:

`CoS(d)=C(S(d))\\\\\\i.e.\\\\\\CoS(d)=C(355d)\\\\\\i.e.\\\\\\CoS(d)=1.5(355d)+2\\\\\\i.e.\\\\\\CoS(d)=532.5d+2`