Business Calculus

Indicate whether the statement is true or false.

1. True or False?

The given table corresponds to the function f(x) = 5

x

– 1.

1~~:x:)====I=~:~.~99=2===~1 ~=~=.9=6===_…L1~~-~:..:..-8::_-~_-_-~1L_..::~_=__=__=__=__~=4=== =__1~!====:I=i=24= ====:1 ===

2. True or False?

The table is filled correctly.

Exponential form Logarithmic form

8-3 =0.001953 log8(0.001953)=3

2

0=1

log2(l) =0

0.4

4 =0.0256

log0.4(0.0256) =4

0.8-

3 = 1.953125 logO.8(1.953125) =3

3. True or False?

)

-x

The given table corresponds to the function f(x) = 0.042( 4.2 – 1~7

1-=—–1—=——–+-=–+—+—-+—-+—-+–3 _J

0.021 ]

Multiple Choice

Identify the choice that best completes the statement or answers the question.

4. Rock Solid Bank & Trust is offering a CD that pays 6% compounded continuously. How much interest

would a $2,000 deposit earn over 10 years? (Round your answer to the nearest dollar.)

Select the correct answer.

a. $3,644

b. $3,639

c. $3,582

d. $1,644

e. $5,644

5. Use logarithms to solve the equation. (Round answers to four decimal places.)

a. x = 0.8333

b. x = -1.8493

c. x = -1.0294

d. x = -0.8333

e. x = 1.0294

6. Encouraged by the popularity of your Dungeons and Dragons website, www.mudbeast.net.you have decided

to charge users who log on to the site. When you charged a $2.00 access fee, your web counter showed a

demand of 170 “hits” per month. After you lowered the price to $1.00, activity increased to 420 hits per

month. Obtain the monthly revenue R as a function of the access fee x.

c.

d.

R = 250×2

-170x

R=250x – ]70

R = -250x

2

– 670x

R = -25Ox + 670

R = -250×2 + 670x

a.

h.

e.

7. Model the data using an exponential function I(x) = Abx

.

I:~=x=)=======~I ~~5=0======1~~=25=======1=~=2=.5======

Select the correct answer.

a. I(x) = 250(0.5rx

h. I(x) = 0.5(250rx

c. I(x) = 250(250)x

d. I(x) = 0.5(0.5)x

e. I(x) = 250(0.5)x

8. The U.S. population was 190 million in 1965 and 260 million in 2000. Assuming exponential population

growth, what will the population be in the year 2025?

Select the correct answer.

a. 1,110 million

b. 270 million

c. 325 million

d. 278 million

e. 555 million

9. Find N, A, and b for the function given.

f(x) = (-x) 0.5 + 5.5 1.6

2

a. N = 4, A = 11, b = 1.6

b. N=11,A=4,b=1.6

c. N= 4, A = 1.6, b = 11

d. N = 1.6,A = 11, b = 4

e. N= 1l,A = 1.6, b =4

10. There are currently 100 cases of Venusian flu in a total susceptible population of 1,000 and the number of

cases is increasing by 22% each day. Find a logistic model for the number of cases of Venusian flu and use

your model to predict the number of flu cases a week from now. Round your answer to the nearest integer.

a. F(7) = 309 cases

b. F(7) = 464 cases

c. F(7) = 525 cases

d. F(7) = 155 cases

e. F(7) = 103 cases

11. For the following demand equation, find the largest possible revenue.

q = -5p + 3,000

a. 600

b. 300

c. 900,000

d. 450,000

e. 360,000

12. Pack-Ern-In Real Estate is building a new housing development. The more houses it builds, the less people

will be willing to pay, due to the crowding and smaller lot sizes. In fact, ifthe company builds 60 houses in

this particular development, it can sell them for $170,000 each, but if it builds 70 houses, it will be able to get

only $160,000 each. What is the largest possible revenue the company can get?

a. $11,500,000

b. $13,351,000

c. $12,981,000

d. $13,225,000

e. $396,750

13. Soon after taking an aspirin, a patient has absorbed 250 mg of the drug. If the amount of aspirin in the

bloodstream decays exponentially, with half being removed every 2 hours, find the time it will take for the

amount of aspirin in the bloodstream to decrease to 180 mg.

Select the answer rounded to three decimal places.

a. 0.528 hours

b. 3.165 hours

c. 1.055 hours

d. 2.110 hours

e. 2.638 hours

14. Plutonium-239 is used as a fuel for some nuclear reactors and also as the fissionable material in atomic

bombs. It has a half-life of 24,400 years. How long will it take 10 grams ofplutonium-239 to decay to 3

grams?

Select the correct answer rounded to the nearest integer.

a. 10,625 years

b. 21,250 years

c. 42,500 years

d. 84,800 years

e. 42,400 years

]5. The Better Baby Buggy Co. has just come out with a new model, the Turbo. The market research department

predicts that the demand equation for Turbos is given by q = -5x + 390 where q is the number of buggies it

can sell in one month if the price is $x per buggy. At what price should it sell the buggies to get the largest

revenue?

Round the result to the nearest dollar.

a. $39

h. $7,605

c. $139

d. $20

e. $195

1 6. Convert the exponential function to the form indicated. Round all coefficients to four significant digits.

/(/) = 23.1(0.996) 1;/(/) = Qoe .kt

a. Qo = 23.2,k = 0.009585

b. Qo = 23.2,k = 0.007726

c. Qo = 23.1,k = 0.005867

d. Qo = 23.1,k = 0.004008

e. Qo =23.1,k =0.002149

17. Choose the logistic function that best approximates the given curve.

y

x

4

-5 -4 -3 -2

f(x) =

8

a.

1+2(0.5-

x

)

b. f(x) =

8

1+ 3( o.s-x)

f(x) =

8

c. 1+ 7( o.s-X)

d. f(x) =

8

1+3(3-

x

)

f(x) =

8

e.

1+7(3-

X)

-1 1 4

18. Find they-intercept(s) of the graph of the quadratic function.

3x

2

– 33x + 84

a. (0,7), (0,4)

b. (7,0), (4,0)

c. (0,84)

d. (84,0)

e. (0,-84)

19. Find an equation for exponential function that passes through the pair of points (4,3) and (7,1).

y =Abx

(b > 0)

a. A == 13.0282,b == 0.5584

b. A == 12.9801,b = 0.6936

c. A = 12.9805,b == 0.6933

d. A == 12.9802,b == 0.6934

e. A == 12.9762,b == 0.6904

Numeric Response

20. The table lists interest rates on long-term investments (based on 10-year government bonds) in several

countries in 2004-2005. Assuming that you invest $15,000 in Japan, how long (to the nearest year) must you

wait before your investment is worth $21,000 if the interest is compounded annually?

V.S. Japan Canada

5.3% 1.5% 5.2%

____ year(s)

21. The graph shows the actual percentage ofV.S. households with a computer as a function of household

income (the data points) and a logistic model of these data (the curve). The logistic model is

P(X) = 95

1 + 5.25(1.05)-x

where x is the household income in thousands of dollars. According to the model, what percentage of

extremely wealthy households had computers?

U.S. house! oios ·…vith a computer (%) ..______

80 ,-r

-”

40

.>

/’

60

/”

•

20 ~o 60 60

– .

Housebote incorne ($1.000)

p= %

—-

7

__ —-‘L

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Posted on May 19, 2016Author TutorCategories Question, Questions