Differences of Accumulated Change
f(x) = 11(0.85x); g(x) = 7(0.75x); a = 2; b = 10
Find the area between the two curves. (Round to 3 decimal places)
23.260
Find the average value of the following function f(x) = 3x2 interval -1 < x < 4.
13
It is estimated that a sunken oil tanker will leak oil into the surrounding waters at a rate of r(t) = (19t + 30) / (1+t3) million gallons per year, t years from the date the vessel sank. How much oil will leak over the first 5 years? (Round to 3 decimal places)
54.860 million gallons
A company will invest 4% of its profit into a fund to fund capital improvements. This account bears 3.8% interest, compounded continuously. The current level of profit is 6 million dollars per year, but the company believes that this amount will increase by 3% per year. What is the flow rate equation?
R(t) = .04(6(1.03t)) million dollars per year
Determine the price at which demand is zero: D(p) = 50-2p
$25
f(x) = 0.24x − 3; g(x) = 13(0.93x); a = 15; b = 50
Solve for the input value(s) at which the graphs of f and g intersect. (Round your answer to three decimal places.)
x = 22.831
Let H(x) be a quantity function.
H(x)= 2 - x2 dollars where x is the number of days after January 1. Find the average rate of change in H(x) over the interval -1 ≤ x ≤ 5 (include units in final answer)
-4 dollars per day
Integrate 9.6x-.432 from .36 to ∞
Diverges
A firm has an annual profit of $4.2 million and allocates 5% of its profits into as a continuous stream into investments. If the profits remain constant, what is the flow rate equation?
R(t) = .05(4.2) million dollars per year
The demand for ceiling fans is given by D(p) = 25.92(0.996p) thousand ceiling fans where p is the price in dollars of a ceiling fan. Compute the price of unit elasticity.
$250 per ceiling fan
f(x) = 0.24x − 3; g(x) = 13(0.93x); a = 15; b = 50
Calculate the total area between the two curves. (Round to 3 decimal places)
140.622
U.S factory sales of electronic goods to dealers from 1990 to 2001 can be modeled as: s(t) = .0388t3 - 0.495t2 + 5.698t +43.6 billion dollars, t years since 1990 Calculate the average value of U.S factory sales from 1990 to 2001 (Round to 3 decimal places).
$67.885 billion
Integrate 3x-2 from 10 to ∞
.3
A company showed a profit of $1.8 million last year. The company expects their profit to decrease by 7% each year over the next 5 years and will be continuously invested into an account with an interest rate of 4.75%. Calculate the 5 year present value (Round to 3 decimal places):
R(t) = 1.8(.93t) million dollars per year
PV = $6.767 million
Given the following supply function, calculate producer revenue and producer surplus at a price of $19.99 s(p) = .2p million dollars when p > 5 s(p) = 0 elsewhere (Round to 3 decimal places)
Producer revenue = $79.920 million
Producer surplus = $37.460
The rate of change of the value of goods exported from a country between 1990 and 2001 can be modeled as E '(t) = −1.664t2 + 16.471t + 7.632 billion dollars per year and the rate of change of the value of good imported into the country during those years can be modeled as I '(t) = 4.918t + 40.861 billion dollars per year.
Calculate the difference between the accumulated value of imports and the accumulated value of exports from the end of 1990 through 2001. (Round your answer to three decimal places.)
$404.824 billion
The circulation of newspapers in the U.S between 1986 and 2000 can be modeled as n(x) = 0.00792x3 - 0.32x2 + 3.457x + 51.588 million newspapers where x is the number of years since 1980 What was the average newspaper circulation from 1986 to 2000? (Round to 3 decimal places)
59.668 million newspapers
A substance will decay at a rate of r(t) = -0.027205(0.998188t) grams per year How much will eventually decay?
15 grams
Last year, a company had a profit of 1.8 million dollars. They expect their profits to decrease by .04 million dollars per year over the next 5 years and will be continuously invested into an account with an interest rate of 4.75%. Find the future value (Round to 3 decimal places):
R(t) = 1.8 - .04t million dollars per year
FV = 9.617 million dollars
D(p) = (40.007) / (1+.033e.354p) million pounds S(p) = (51) / (1 + 53.98e-.395) million pounds when p > .5 Find market equilibrium price and quantity (Round to 3 decimal places)
$9.26 per pound
21.318 million pounds
f(x) = 3.7(1.194x) and g(x) = .04x3 - .54x2 2.5x + 4.47
Calculate the total area of the shaded regions (Round to 3 decimal places)
Intersection point: x = 4.651
Total area = 27.653
During a certain summer thunderstorm, the temperature drops and then rises again. The rate of change of the temperature during the hour and a half after the storm began is given by t(h) = 9.32h3 − 15.54h2 + 17.34h − 9.97 where output is measured in °F per hour and h is the number of hours since the storm began.
If the temperature was 80°F at the time the storm began, what was the average temperature during the first 1.5 hours of the storm? (Round your answer to three decimal places.)
77.014 oF
The rate of change of the value of an antique chair is r(t) = 2500/(x1.5) dollars per year where x is the age of the chair in years. The chair was valued at $300 25 years after it was crafted. How much will the value increase between 25 and 100 years after being crafted? How much will the chair be worth 100 years after it was crafted?
A. $500
B. $800
A firm has a flow rate equation of R(t) = .03(2(.95t)) billion dollars per year. How much will the corporation invest over the next 20 years? (Round to 3 decimal places)
$0.750 billion
D(p) = 38.301 / (1 + .003e.050p) million calculators S(p) = .747p - 35.467 million calculators when p > 47.5 Calculate producer surplus, consumer surplus, and total social gain at market equilibrium (Round to 3 decimal places):
PS: 606.026 million dollars
CS: 1184.337 million dollars
TSG: 1790.363 million dollars