Math 180 (Business Calculus)

Test #3Summer2021*Show all relevant works for full credit

1.(a)A note will pay $40,000 at maturity 5 years from now.howmuch should you be willing to pay for the note now if money is worth6.2% compounded continuously?

(b)Theradio activecarbon-14 in an organism decays according

tothe equation,

A =A0e- 0.000124t

wheretis time in years andA0is the initial amount of carborn-14present att=0(the time of death) Find the half-life of radioactive carbon-14(the time it takes for a certain amount of carbon -14 to decay to half the original amount.

2.Find the derivative of each function.

(a)f(x) = 2e3x(b) y = ln 5x(c) y = log4x(d)h(x) = 8x

3.(a)Find the derivative of the function. Write answer in simplifiedform .y=4x- 3

3x+5

3(b) Find thederivativef(x) = log6( 3x2)

4.Find the derivative of each function.

(a)x3-5

x3(b)(3x2-10)4

(c)(3x+2)

5.(a) Find the derivative of the function y = log5(4x2)

(b)Find the derivative ofofthe functionx4ex.Give answer in simplified factored form.

6(a) Use implicit differentiationtofinddy/dx for the function:

xy+ 3y -5y2=10.Simplify your answer.

( b) Use implicit differentiation to finddy/dx for x2+ y3- 4 = 5.

Then find the slope of the curve at (-1,2)

7(a) A point is moving on the graph ofy2- 4x2= 12 so that its x-coordinate is decreasing by2unitspersecond when (x,y) is (1,4)find the rate of change of the y-coordinate.

(b)A 17- foot ladderis placedagainst a wall. If the foot of the ladderis pushedtoward the wall at 0.5 foot per second, how fast is the top of the ladderrising when the foot is 8 feet from the wall?

8.(a)A rock thrown into a still pond causes a circular ripple.If the radius of the ripple is increasing by 2 feet per second howfastis he area changing when the radius is 10 feet?(Areaof acircle=r2)

(b).A sphericalbasket ballis deflating. If the radius is decreasing at 2millimeters per second,how fast is the volume changing when the radius is 10 millimeters.(Volumeof a sphere=4(3)

3

9(a)Ifan object moves along the y-axis (scale in feet) so that it is at

Y =8x2-4x + 1at time x seconds

Find the instantaneous velocity function, then evaluate the velocity at time x= 4 seconds.

9(b)AtFord Motors assembly, a new employee,on the average is , is able to assemble

N(t) = 10(1- e-0.4t) units after t day oftraining.

What is the rate of learning after 3 days?

10(a) A model for the average income perhouseholdbeforetaxes are paid isf(t) = 1,900t +22,500 wheretis years since 1990, find the percentage rate of change of household income in 2020 . Round your answer to the hundredths.

10(b)Theprice -demand equation for home delivered large pizzas is

p = 38.2 -0.002x

wherexis the number of pizzasdelivered weekly. The current price of one pizzais$21. In order to generate additional revenue from the sales of large pizza, will you recommend an increase or decrease inprice?Explain