Project #155986 - Written Assignment III

Mathematics Tutors

Subject Mathematics
Due By (Pacific Time) 11/25/2016 12:00 am

Written Submission 

Present all relevant work in your own handwriting in the space provided for each problem. Where necessary, your answers must be presented using grammatically correct, complete English sentences.

1. Monthly sales of a particular computer are expected to decline at the following rate:
S (t ) = 45t 2 3 60, where t is time in months and S(t) is the number of computers sold each month. The company plans to stop manufacturing this computer when monthly sales reach 800 computers.

a) If monthly sales now (t = 0) are 2,420 computers, find S(t).

b) Use a graphing calculator to approximate the solution of the equation S (t ) = 800. Round to two decimal places as needed. Write your keystrokes and circle your answer value with appropriate units.

2. In order to study the effects of World War II on a certain country’s economy, an economist used data from that county’s census bureau to produce the following Lorenz curves for the distribution of income in 1935 and 1947.

f(x)=x2.6 Lorenzcurvefor1935

g ( x ) = x1.3 Lorenz curve for 1945
Find the Gini index of income concentration for each Lorenz curve and interpret the results.

NO CREDIT will be given for correct answers without both algebraically correct work that

directly and strongly supports your answer and sufficient calculus-based supporting work.

3. A business is planning to purchase a piece of equipment that will produce a continuous stream of income for 8 years with rate of flow f (t ) = 9, 000. If the continuous income stream earns

6.85%, compounded continuously, what single deposit into an account earning the same interest rate will produce the same future value as the continuous income stream? This deposit is called the present value of the continuous income stream.

4. Find the consumers’ surplus and the producers’ surplus at the equilibrium price level for the 0.005 x 0.005 x

price-demand equation: p = D(x) 110e= ; and price-supply equation: p = S (x) 20e = .

Round all values to the nearest integer. Include a graph that identifies the consumers’ surplus and the producers’ surplus.

Do the work on a paper with all step of calculation, and send it back to me.

 

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