3 maths problems

(i need steps, thx)

1.Suppose the total cost of producing q units of some commodity is given by the cost function C(q)=0.003q^2+5q+110, where q is the number of units produced, and C(q) is the total cost, in dollars, to produce q units.

A) Find a simplified expression for the marginal cost function. (Be sure to use the proper variable in your answer.)

MC(q)= ________

B) What is the exact rate of change of costs when 700 units have been produced?

The rate of change is dollars per item. (Your answer may be negative.)


2.Suppose the demand for a product is given by D(p)=−6p+152.

A) Calculate the elasticity of demand at a price of $5. (Give your answer to three decimal places.)

Elasticity = _________

B) At what price do you have unit elasticity? (Round your answer to the nearest penny.)

Price = $ ___________

3.When an initial amount of money, A, in dollars, is invested into an account that earns interest continuously, the Future Value of the account after t years is given by the formula: F(t)=Ae^rt, where r is the annual interest rate earned by the account. Let A=$21,000 and r=9.3%.

A) What is the value of the account, in dollars, after 10 years? Give your answer rounded to two decimal places.

Answer $ ______

B) What is the exact instantaneous rate of change of the value of the account at exactly 11 years? Give your answer rounded to two decimal places.

Answer: ________dollars per year

C) At what time, in years, is the instantaneous rate of change of the value of the account increasing by $7,880.31 per year? If necessary, round your answer to two decimal places.

Answer: ______After years.

D) What is the average rate of change of the future value of the account between year 10 and year 14? (Round to the nearest penny/cent.)

Answer: ________dollars per year. (Round to two decimal places.)