Question 1

Suppose the world demand for iron is about 420,000,000 tons per year. The known global reserves are 100,000,000,000 tons. What is the static reserve for iron?

Accepted Answer

To find the static reserve for iron, we divide the known global reserves by the annual demand:

Static reserve = Known global reserves / Annual demand
Static reserve = 100,000,000,000 / 420,000,000 
Static reserve ≈ 238.1

Therefore, the static reserve for iron is approximately 238.1 years. The answer is C.

Question 2

Suppose the world demand for silver is about 343,750,000 troy ounces per year. The known global reserves are 5,500,000,000 troy ounces. What is the static reserve for silver?

Accepted Answer

The static reserve for silver can be calculated by dividing the known global reserves by the annual world demand: 
Static reserve = 5,500,000,000 / 343,750,000 = 16. 
Therefore, the answer is C.

Question 3

The population of the United States in 1700 was about 600,000,000. In 2000, the population was about 6,000,000,000. What was the average growth rate over that period?

Accepted Answer

To calculate the average growth rate, we can use the formula: 
[(Ending Population / Beginning Population)^(1/Number of Years)] - 1

Plugging in the numbers, we get:
[(6,000,000,000 / 600,000,000)^(1/300)] - 1
= (10^(1/300)) - 1
= 0.0077 or 0.77%

Therefore, the average growth rate over that period was 0.77%, which corresponds to choice B.

Question 4

Suppose the world demand for copper is about 8,600,000 tons per year. The known global reserves are 308,000,000 tons. The demand for copper is increasing at a rate of 4.6%. What is the exponential reserve for copper?

Accepted Answer

The exponential reserve is calculated using the formula: Reserves / (Annual Demand * (1 + Growth Rate)). Plugging in the values: 308,000,000 / (8,600,000 * 1.046) ≈ 21.62 years.

Question 5

Suppose the world demand for silver is about 343,750,000 troy ounces per year. The known global reserves are 5,500,000,000 troy ounces. The demand for silver is increasing at a rate of 2.7%. What is the exponential reserve for silver?

Accepted Answer

The answer of Suppose the world demand for silver is...

Question 6

Use the following reproduction curve for a population to answer the Questions Units are in thousands. 
-The maximum sustainable yield is approximately:

Accepted Answer

The answer of Use the following reproduction curve for a...

Question 7

The population of Ontario in 1997 was about 11,249,500. In 2001, the population was about 11,874,400. What was the average growth rate over that period?

Accepted Answer

To find the average growth rate, we need to use the formula:

Average Growth Rate = (Ending Value / Beginning Value)^(1/number of years) - 1

Plugging in the numbers, we get:

Average Growth Rate = (11,874,400 / 11,249,500)^(1/4) - 1
Average Growth Rate = 1.056^0.25 - 1
Average Growth Rate = 0.0136 or 1.36%

Therefore, the best choice is B, with an explanation that shows the calculation using the formula for average growth rate.

Question 8

The half-life of iron-59 is 45 days. After three months, how much of a 72-gram sample of iron-59 is left?

Accepted Answer

First, we need to find out how many half-lives have passed in three months:

1 half-life = 45 days 
3 months = 90 days

90 days / 45 days per half-life = 2 half-lives

So, after 2 half-lives, the amount of iron-59 remaining is:

1/2 x 1/2 = 1/4

So, the amount remaining is:

72 grams x 1/4 = 18 grams

Therefore, the answer is B, 18 grams.

Question 9

Suppose the world demand for cobalt is about 16,360,000 pounds per year. The known global reserves are 1,800,000,000 pounds. The demand for cobalt is increasing at a rate of 1.5%. What is the exponential reserve for cobalt?

Accepted Answer

The exponential reserve for cobalt can be calculated using the formula:

Exponential reserve = [Known reserves / (Annual demand x (1 + annual increase rate))]^(1/annual increase rate)

Plugging in the given values, we get:

Exponential reserve = [1,800,000,000 / (16,360,000 x (1 + 0.015))]^(1/0.015)

Exponential reserve = 65.47

Therefore, the best choice is C) 65.47.

Question 10

Suppose the world demand for copper is about 8,600,000 tons per year. The known global reserves are 308,000,000 tons. What is the static reserve for copper?

Accepted Answer

The static reserve is calculated by dividing the known global reserves by the annual demand. 308,000,000 tons / 8,600,000 tons per year = 35.81 years.

Question 11

Suppose the world demand for cobalt is about 16,360,000 pounds per year. The known global reserves are 1,800,000,000 pounds. What is the static reserve for cobalt?

Accepted Answer

The answer of Suppose the world demand for cobalt is...

Question 12

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?

Accepted Answer

Using the formula for half-life decay:

Nt = N0 * (1/2)^(t/T)

where Nt is the final amount, N0 is the initial amount, t is the time elapsed, and T is the half-life.

Plugging in the given values:

1 = 10 * (1/2)^(t/8)

Taking the logarithm of both sides:

log(1) = log(10) + (t/8) * log(1/2)

0 = 1 - (t/8) * 0.301

Solving for t:

t = (1/0.301) * 8

t ≈ 26.6 days

Therefore, the answer is C.

Question 13

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?

Accepted Answer

The exponential reserve is calculated by dividing the known reserves by the annual demand and adjusting for the growth rate. Using the formula: Reserve / (Demand * (1 + growth rate)), we get 100,000,000,000 / (420,000,000 * 1.018) ≈ 93.3 years.

Question 14

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 iron-59 is 45 days and its biological half-life is 600 days. Find the effective half-life of iron-59.

Accepted Answer

Using the formula, we have
$$\frac{1}{H_e}=\frac{1}{H_p}+\frac{1}{H_b}=\frac{1}{45}+\frac{1}{600}$$
$$\frac{1}{H_e}=\frac{8}{360}+\frac{3}{360}=\frac{11}{360}$$
$$\Rightarrow H_e=\frac{360}{11}=32\frac{8}{11}\approx \boxed{41.9 \text{ days}}$$

Question 15

If $\ { H } _ { p }$ is much larger than $H _ { b }$ for a particular element, then $H _ { e }$ is approximately equal to:

Accepted Answer

The answer of If \(\ { H } _ {...

Question 16

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.

Accepted Answer

Using the formula for effective half-life, we have:

\begin{align*}
\frac{1}{H_e}&=\frac{1}{H_p}+\frac{1}{H_b}\
\frac{1}{H_e}&=\frac{1}{87.4	ext{ days}}+\frac{1}{90	ext{ days}}\
\frac{1}{H_e}&\approx0.02285	ext{ days}^{-1}\
H_e&\approx43.8	ext{ days}\
\end{align*}

Rounding to one decimal place, we get the effective half-life of sulfur-35 to be 44.3 days. Therefore, the answer is A).

Question 17

Suppose the world demand for chromium is about 1,845,000 tons per year. The known global reserves are 775,000,000 tons. The demand for chromium is increasing at a rate of 2.6%. What is the exponential reserve for chromium?

Accepted Answer

The answer of Suppose the world demand for chromium is...

Question 18

Suppose the world demand for chromium is about 1,845,000 tons per year. The known global reserves are 775,000,000 tons. What is the static reserve for chromium?

Accepted Answer

To find the static reserve, we divide the known global reserves by the world demand.
Static reserve = Known global reserves / World demand
= 775,000,000 / 1,845,000
= 420.05
Therefore, the static reserve for chromium is 420.05.

Question 19

If $\ { H } _ { p } /H _ { b }$ is approximately equal to 1, then $H _ { e }$ is approximately equal to:

Accepted Answer