Final answer:
The cost of cleaning up x percent of an oil spill can be modeled by the equation C(x) = mx. Using the data provided, we can find the value of the constant m and use the model to predict the percentage of an oil spill that can be cleaned up with a given budget.
Step-by-step explanation:
The cost of cleaning up x percent of an oil spill can be modeled by the equation C(x) = mx, where C(x) is the cost in dollars and x is the percentage of the spill being cleaned up. In this case, the company has data that spending $400,000 will clean up 70% of an oil spill. We can use this information to find the value of m.
Given that C(70) = 400,000, we can substitute these values into the equation: 400,000 = 70m. Solving for m, we find that m = 400,000/70 = 5,714.29. Therefore, the value of m is approximately 5,714.29.
To predict the percentage of an oil spill that can be cleaned up if the company's budget is $800,000, we can use the equation C(x) = mx. Substituting the value of m, we have C(x) = 5,714.29x. We can solve for x by setting C(x) equal to $800,000 and solving for x: 800,000 = 5,714.29x. Dividing both sides by 5,714.29, we find that x = 800,000/5,714.29 = 140.
Therefore, if the company's budget is $800,000, they can clean up approximately 140% of an oil spill.