Test #3 (Chapters5/6) Math 180 -Business CalculusSummer2021

Due11:59pm,Wednesday07/28/21

Show all worksforfulland partialcredit.

Name of Student____________________________________________________________

1(a).Findthe equation of the curve that passesthrough(2,8) if the slope of the curve is given bydy/dx = 2x3

1(b).Find the revenue functionR(x)when the marginal revenue is

R'(x) = 500-0.05x

andno revenue results at zero production level?What is the revenue at a production level of1,500 units?

2(a). The rate of change of the monthly sales ofnewNikeshoeis

S'(t) =500 t1/4;S(0) =0wheretis the number of months since the shoe was released,andS(t)is the number of shoes sold each month.

FindS(t).When will the monthly sales reach 20,000?

2(b)Theequation of the marginal cost function for the production ofxthousand sunglasses is

C' (x)=3x2- 24x + 53

Find the cost functionifmonthlyfixed cost at 0 output is $ 80,000. What is the cost of manufacturing 6,000 sunglasses permonth.?

3(a)The marketing research department ofanautomobile manufacturing companyestimates that sales in million dollars will increase at the monthly rate ofrate ofS'(t) = 10(1-e-0.1t)0tmonths after the initial sales of the car.

What will be the total sales10months after theintroduction of the car if we assume no sales at the introduction of thecar.

3(b)Theprojected rate of increase of in enrollment at anew college is estimated bydE/dt= 5000(t+1)-3/2t0,whereE(t) is theprojected enrollment intyears. Ifenrollment is 2,000 now (t=0 )Find the projected enrollment 20 years from now.

4(a)Find the amount A in an account after10years ifdA/dt=0.01A andA(0) = 5,250

4(b)Find the amount A in an account after8years ifdA/dt=rAA(0) =5,000 and A(5) =52,82 .70

5(a) Find the average value off(t) =5over the interval [-2 , 3]

5(b) if the temperatureinanaquarium (in degree Celsius) is given by

C(t) = t3-2t +100

Over a 2-hour period. Find the average temperature over this period?.

6(a)Find the total income produced bycontinuousincomestream in the first 3yeas if the rate of flow is f(t) = 800e0.05t

6(b)Aproduction manager obtained the following function for the rate of labor use;

L'(x) = 2,400x-1/2

Approximate ,how many labor hourswill be required to assemble the17ththrough the 25thcontrol units.[Hint: let a=16 and b =25]

(7a) The rate ofincreaseinmaintenance costs in dollars per year for a particular apartment is given by

M' (x)=f)x) = 80x2+ 6,000

Wherexis the age of the apartment complex in years andM(x)is the total accumulated cost forxyears.

Write a definite integral that will give the total cost of maintenance from the end of the second year to the end of the seventhyearandevaluatethe integral.

7(b)The rate at which the total amount of money put into an advertising campaign is changing is givenbyA'(t)wheretis the number of days since the campaign began. What doesdtrepresent ?

8(a)The total accumulated cost C(t)and revenue R(t) (in thousands of dollars),respectively,for a bakerysatisfyC'(t) = 3andR'(t) = 15e-0.3twheretis the number of years that the bakery had been in operation. Find the useful life of thebakery{C'(t) =R'(t)}to the nearest year.

8(b)Whatis the total profit accumulated during the useful life of the bakery in #8(a)?

9(a) Find the area between the graph off(x)= x2- 25 and the x axis over the interval[ 3,7]

9(b) Find the area bounded byf(x)=8-x2andg(x) = 2x

10(a)Evaluate the DefiniteIntegral :+2et-3t-1)dt

10(b) Integrate by parts:e4xdx