There will be three international calculus problems that this group will present. These three problems will each be from separate countries:
Tibet (filmed on Pike's Peak)
France (filmed in Rocky Mountain National Park)
Iceland (filmed at a log cabin in Rocky Mountain National Park)
The three problems are as follows:
1. (p. 428) The Tibetan Game Commission releases 40 elk into a game refuge. After 5 years, the elk population is 104. The commission believes that the environment can support no more than 4000 elk. The growth rate of the population p will be provided in our newscast.
(a) Write a model for the elk population in terms of t.
(b) Use the model to estimate the elk population after 15 years.
(c) Find the limit of the model as t approaches infinity.
2. (p. 416) Suppose an experimental population of fruit flies increases according to the law of exponential growth. There were 100 flies after the second day of the experiment and 300 flies after the fourth day. Approximately how many flies were in the original population?
3. (p. 225) A cabin in Keflavikurflugvollur, Iceland is constructed using wooden beams. These beams need to be designed to withstand the weight of the entire cabin to make the cabin safe for visitors. A wooden beam has a rectangular cross section of height h and width w. The strength S of the beam is directly proportional to the width and the square of the height. What are the dimensions of the strongest beam that can be cut from a round log of diameter 24 inches? (Hint: S = (k)(h^2)(w), where k is the proportionality constant.)
There will be three international calculus problems that this group will present. These three problems will each be from separate countries:
The three problems are as follows:
1. (p. 428) The Tibetan Game Commission releases 40 elk into a game refuge. After 5 years, the elk population is 104. The commission believes that the environment can support no more than 4000 elk. The growth rate of the population p will be provided in our newscast.
(a) Write a model for the elk population in terms of t.
(b) Use the model to estimate the elk population after 15 years.
(c) Find the limit of the model as t approaches infinity.
2. (p. 416) Suppose an experimental population of fruit flies increases according to the law of exponential growth. There were 100 flies after the second day of the experiment and 300 flies after the fourth day. Approximately how many flies were in the original population?
3. (p. 225) A cabin in Keflavikurflugvollur, Iceland is constructed using wooden beams. These beams need to be designed to withstand the weight of the entire cabin to make the cabin safe for visitors. A wooden beam has a rectangular cross section of height h and width w. The strength S of the beam is directly proportional to the width and the square of the height. What are the dimensions of the strongest beam that can be cut from a round log of diameter 24 inches? (Hint: S = (k)(h^2)(w), where k is the proportionality constant.)