Exam 23: The Economics of Resources

Suppose the world demand for copper is about 8,600,000 tons per year and the static reserve is about 36. However, the demand for copper is increasing at a rate of 4.6%. What is the exponential reserve for copper?

Suppose the world demand for silver is about 343,750,000 troy ounces per year and the static reserve is 16. However, the demand for silver is increasing at a rate of 2.7%. What is the exponential reserve for silver?

The population of the United States in 2000 was about 281,422,000. In 2001, the population was about 284,797,000. What was the average growth rate over that period?

Suppose the world demand for gold is about 32,000,000 troy ounces per year. The known global reserves are 100,000,000,000 troy ounces. What is the static reserve for gold?

A population grows according to a logistic growth model, with population parameter  = 1.4 and x = 0.05 for the first year. Find the value of x after the third year.

Use the following reproductive curve for a population to answer the Questions. Units are in thousands. -Estimate the equilibrium population size.

A population grows according to a logistic population model, with population parameter  = 3.7 and starting population fraction x = 0.8 for the first year. The value of x after the second year is:

Suppose the world demand for iron is about 420,000,000 tons per year. The known global reserves are 100,000,000,000 tons. The demand for iron is increasing at a rate of 1.8%. What is the exponential reserve for iron?

Use the following reproduction curve for a population to answer the Questions Units are in thousands. -The sustainable yield corresponding to a population of size 10,000 remaining after the harvest is approximately:

The population of the world in 1800 was about 900,000,000. The average growth rate from 1800 to 1900 was 0.51%. What was the approximate population in 1900?

Use the following information to answer the Questions A radioactive element used in medicine has a physical half-life $H_{p}$ (the time in which half of any quantity of the element decays) and a biological half-life $H _ { b }$ (the time in which half of an amount of this element in the body is excreted). The effective half-life $H _ { e }$ is calculated from $\frac { 1 } { H _ { e } } = \frac { 1 } { H _ { p } } + \frac { 1 } { H _ { b } } .$ -The physical half-life of sulfur-35 is 87.4 days and its biological half-life is 90 days. Find the effective half-life of sulfur-35.

Radon-222 has the half-life $H = 3.82$ What is the decay constant $\lambda$ ?

A colony of penguins had 534 members at the beginning of 1998. At the beginning of 2015, the colony had grown to 821 members. What was the average growth rate over that period?

A population grows according to a logistic population model, with population parameter  = 1.3 and starting population fraction x = 0.7 for the first year. The value of x after the second year is:

Use the following reproductive curve for a population to answer the Questions. Units are in thousands. -Estimate the sustainable yield corresponding to a population of size 40,000 remaining after the harvest.

The half-life of radon-222 is 3.82 days. How long will it take for a quantity of radon-222 to decay to one millionth of the original amount?

Use the following reproductive curve for a population to answer the Questions . Units are in thousands. -Estimate the equilibrium population size.

Iodine-131 has a half-life of eight days. A sample that originally contained 10 grams of iodine-131 now contains 1 gram. How much time elapsed between the two measurements?

Suppose that the discrete logistic model for population growth is models as follows: $P _ { n + 1 } = P _ { n } + 0.351 P _ { n } \left( 1 - \frac { P _ { n } } { 2.849 \times 10 ^ { 8 } } \right)$ What is the natural rate of increase when the population is small?

Use the following reproductive curve for a population to answer the Questions. Units are in thousands. -Estimate the maximum sustainable yield.