Population calculation worksheet featuring questions on demographics and growth rates for Pennsylvania and several countries.

Let's solve the Population Calculation Worksheet step by step, using the given data.

---

Given Information:

- Population of Transylvania = 2.3 million people
→ $ 2,300,000 $
- Area = 800,000 square miles
- Number of births in one year = 109,000
- Number of deaths in one year = 111,000

---

Question 1: What is the current population density?

Population Density = $ \frac{\text{Population}}{\text{Area}} $

$$
= \frac{2,300,000}{800,000} = 2.875 \text{ people per square mile}
$$

✔ Answer: 2.875 people/sq mi

---

Question 2: What are the birth and death rates?

We calculate birth rate and death rate per 1,000 people.

#### Birth Rate = $ \frac{\text{Number of births}}{\text{Population}} \times 1000 $

$$
= \frac{109,000}{2,300,000} \times 1000 = 47.39 \text{ per 1,000 people}
$$

#### Death Rate = $ \frac{\text{Number of deaths}}{\text{Population}} \times 1000 $

$$
= \frac{111,000}{2,300,000} \times 1000 = 48.26 \text{ per 1,000 people}
$$

✔ Answer:
- Birth Rate: 47.39 per 1,000
- Death Rate: 48.26 per 1,000

---

Question 3: What is the population growth rate (r)?

Growth Rate (r) = Birth Rate − Death Rate

$$
r = 47.39 - 48.26 = -0.87 \text{ per 1,000}
$$

So, the population is decreasing at a rate of 0.87 per 1,000 people per year.

To express as a percentage:

$$
r = \frac{-0.87}{1000} = -0.087\% \text{ per year}
$$

✔ Answer: -0.87 per 1,000 or -0.087% per year

---

Question 4: In how many years will the population double?

This uses the Rule of 70, which estimates doubling time:

$$
\text{Doubling Time} = \frac{70}{\text{Growth Rate (%)}}
$$

But here, the growth rate is negative (-0.087%), so the population is not growing — it's declining.

Therefore, the population will never double under this rate.

✔ Answer: The population will not double; it is decreasing.

---

Question 5: Calculate the growth rates and doubling times for the countries listed below.

We use:
- Growth Rate (r) = Birth Rate − Death Rate (per 1,000)
- Doubling Time = $ \frac{70}{r} $, only if $ r > 0 $. If $ r \leq 0 $, doubling time is undefined (population not growing).

Let’s compute each:

| Country | Birth Rate | Death Rate | Growth Rate (r) | Doubling Time |
|------------------|------------|------------|------------------|---------------|
| United States | 13 | 8 | 13 - 8 = 5 | $ 70 / 5 = 14 $ |
| Mexico | 19 | 5 | 19 - 5 = 14 | $ 70 / 14 = 5 $ |
| Japan | 8 | 9 | 8 - 9 = -1 | N/A (declining) |
| United Kingdom | 13 | 9 | 13 - 9 = 4 | $ 70 / 4 = 17.5 $ |
| China | 12 | 7 | 12 - 7 = 5 | $ 70 / 5 = 14 $ |
| India | 23 | 7 | 23 - 7 = 16 | $ 70 / 16 = 4.375 $ |
| Nigeria | 41 | 16 | 41 - 16 = 25 | $ 70 / 25 = 2.8 $ |
| South Africa | 21 | 14 | 21 - 14 = 7 | $ 70 / 7 = 10 $ |
| Canada | 11 | 7 | 11 - 7 = 4 | $ 70 / 4 = 17.5 $ |
| Italy | 9 | 10 | 9 - 10 = -1 | N/A (declining) |

✔ Final Table:

| Country | Birth Rate | Death Rate | Growth Rate (r) | Doubling Time |
|------------------|------------|------------|------------------|---------------|
| United States | 13 | 8 | 5 | 14 |
| Mexico | 19 | 5 | 14 | 5 |
| Japan | 8 | 9 | -1 | N/A |
| United Kingdom | 13 | 9 | 4 | 17.5 |
| China | 12 | 7 | 5 | 14 |
| India | 23 | 7 | 16 | 4.375 |
| Nigeria | 41 | 16 | 25 | 2.8 |
| South Africa | 21 | 14 | 7 | 10 |
| Canada | 11 | 7 | 4 | 17.5 |
| Italy | 9 | 10 | -1 | N/A |

> ⚠️ Note: Doubling time is only meaningful when the growth rate is positive.

---

✔ Summary of Answers:

1. Population Density: 2.875 people per square mile
2. Birth Rate: 47.39 per 1,000, Death Rate: 48.26 per 1,000
3. Growth Rate (r): -0.87 per 1,000 (or -0.087%)
4. Doubling Time: Not possible (population is declining)
5. See completed table above.

Let me know if you'd like this formatted as a printable worksheet!