Reference no: EM131076331
Exponential Growth and Decay; Related Rates
Problem 1- The half-life of cesium-137 is 30 years. Suppose we have a 100-mg sample.
(a) Find the mass that remains after t years.
(b) How much of the sample remains after 100 years?
(c) After how long will only 1 mg remain?
Problem 2- A curve passes through the point (0, 5) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve?
Problem 3- The radius of a sphere is increasing at the rate of 4 mm/s. How fast is the volume increasing when the diameter is 80 mm?
Problem 4- If x2 + y2 + z2 = 9, dx/dt = 5, and dy/dt = 4, find dz/dt when (x, y, z) = (2, 2, 1).
Problem 5- A particle moves along the curve y = 2 sin(πx/2). As the particle passes through the point (1/3, 1), its x-coordinate increases at a rate of √10 cm/s. How fast is the distance from the particle to the origin changing at this instant?
Problem 6- Water is leaking out of an inverted conical tank at a rate of 10,000 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 m, find the rate at which water is being pumped into the tank.
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All income in economy is either profit income or wage income
: Firm C produces 1,000 pounds of cotton at a cost of 50 cents per pound. They sell all of the cotton to Firm S for 75 cents per pound. Firm S makes 1,000 t-shirts with the cotton for a total cost of $1.50 per t-shirt. There are no other firms in this ..
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How long would it take giant tortoise to travel five meters
: A giant tortoise can walk about 1/10 meter per second on land. A cooter turtle can walk about 1/2 per second on land. how long would it take a giant tortoise to travel five meters?
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Case of managerial hubris
: For this assignment, read the case study, "The 1920 Farrow's Bank Failure: A Case of Managerial Hubris." This case is located in the ABI/Inform Complete database found in the CSU Online Library (see reference below). Hollow, M. (2014). The 1920 Fa..
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The real price of movie ticket was the same in both years
: In 1976 a movie ticket was $4 and the price index was 56. In 2009 a movie ticket was $9 and the price index was 228. Based on this information: The real price of a movie ticket was the same in both years.
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Find the rate at which water is being pumped into the tank
: Water is leaking out of an inverted conical tank at a rate of 10,000 cm3/min at the same time that water is being pumped into the tank at a constant rate. find the rate at which water is being pumped into the tank
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All income in economy is either profit income or wage income
: Firm C produces 1,000 pounds of cotton at a cost of 50 cents per pound. They sell all of the cotton to Firm S for 75 cents per pound. Firm S makes 1,000 t-shirts with the cotton for a total cost of $1.50 per t-shirt. They sell all of the shirts to Fi..
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Sufficient to increase our population standard of living
: My contention is the US is not expanding its production possibilities enough to lead to an increase in our PPC sufficient to increase our population’s standard of living. List two policies that the US government could use that would likely increase o..
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Why the government keeps these import restrictions in place
: In 2013, U.S. sugar imports are restricted by way of an import quota. The domestic sugar price is kept above the world market price of sugar by way of a federal domestic price guarantee. IN comparing the cost or benefit of every job saved in the suga..
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