Hello I need help with my hw is about marginal analysis I didn't understand my professor so I would like to see the steps so I can know how to do these exercises.

Question #1

The concentration of oil diminishes 1%for every 0.5 miles from specific point in the Caribbean Sea where the concentration reached 20% due to a platform leak.

a)Find a model for the concentration distribution after any number of miles.

b)how much of oil can be found 5 miles away from the leak

C) how far we can still find 0.5% of oil in the sea water?

Question #2

Theprice(incents)forapoundofsugarattheInternationalmarketcanbemodeledbythefunction:y=0.0052x^2-0.12x+6.25cents,wherexareyearsafter1960.

a) find the average rate of change of the price of sugar from 1980 to 1990.

b) estimate the rate of increase the sugar price in 2020.

Question #3

A student spends:

E (x) =x+0.25 (x)^2 kilo dollars for x terms for the related school fees. At the present time , it has been taken 5 semrsters. Find the cost of the fees , if the student takes an extra term (6th term). Use E (6)-(5), and marginal analysis. Compare your results. If the difference is more than expected, explain the result.

Question #4

The weekly cost to produce x specific product is given by

C (x) =8000 +100x-0.03x^2 +0.000005x^3, for 1x10000

While the demand function for this specific product is given by,

P (x)=200-0.005x, for 1x10000

Determine the marginal cost, marginal revenue and marginal profit when 2500 items are sold. Assume that the company sells exactly what they produce.