Population calculation worksheet featuring key formulas and examples for demographic analysis.

It looks like you've uploaded a Population Calculation Worksheet that includes various formulas and practice problems related to population dynamics. Since I can't view images directly, I’ll solve the problem based on the text you provided.

Here’s the content from your worksheet:

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POPULATION CALCULATION WORKSHEET

You will need to be familiar with these equations for your Unit 3 Exam and the AP Exam.

#### POPULATION DENSITY
$$
\text{Density} = \frac{\text{Population}}{\text{Area}}
$$

For example:
- $ \frac{270,000,000}{11,000,000 \text{ sq km}} = 25 \text{ people per square kilometer} $

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#### BIRTH OR DEATH RATES
$$
\text{Birth or Death Rate} = \left( \frac{\# \text{ of births or deaths per year}}{\text{total population}} \right) \times 1000 = \text{Birth or Death Rate}
$$

NOTE: To find Crude Birth/Death Rates, multiply the rate by 1,000.
- Example: $ \frac{24,500}{650,000} \times 1000 = 37.7\% $
- So, 37.7 births per 1,000 people per year

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#### FINDING POPULATION GROWTH RATE (GR)
(Use this formula when given birth and death rates)
$$
\text{Growth Rate (GR)} = \text{Birth Rate} - \text{Death Rate}
$$
Or:
$$
\text{GR} = \left( \frac{\text{births} - \text{deaths}}{\text{total population}} \right) \times 1000 = \% \text{ growth rate}
$$

Example:
- $ \frac{10 - 8}{100} \times 1000 = 20 $ → 20‰
- Or: $ \frac{25,500 - 22,500}{650,000} \times 1000 = 4.6\% $

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#### FINDING THE DOUBLING TIME OF A POPULATION – THE RULE OF 70!
(Only apply if the population is growing constantly)

$$
\text{Doubling Time (in years)} = \frac{70}{\text{growth rate (\%)}} = \text{years}
$$

Example:
- If GR = 2%, then doubling time = $ \frac{70}{2} = 35 $ years

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#### FINDING FUTURE POPULATION FROM GROWTH RATE
(Initial population) × (growth rate) = Final Population

NOTE: You must convert % to decimal!
- e.g., 2.7% → 0.027

So:
$$
\text{Future Pop} = P \times (1 + r)^t
$$
Where:
- $ P $ = initial population
- $ r $ = growth rate (as a decimal)
- $ t $ = time in years

Example:
- $ 650,000 \times (1 + 0.027)^{10} = ? $

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Population Problem – SHOW ALL WORK!

Given the following information, answer questions 1–3.

> There are currently 250,000 inhabitants of the island. Last year, there were 12,000 new children born and 10,000 people who moved into the island.

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Questions:

1. What is the current population density?

2. What are the birth and death rates?

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Let’s solve each step-by-step.

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✔ Question 1: What is the current population density?

We are told:
- Current population = 250,000
- But we don’t have the area of the island.

Wait — no area is given in the problem.

That means either:
- The area is missing, or
- We’re supposed to assume it's not needed, or
- It might be implied elsewhere.

But since no area is provided, we cannot calculate population density unless more data is given.

However, let's double-check: Is there any mention of area?

No — only:
- Population: 250,000
- Births: 12,000
- Deaths: Not mentioned
- Migration: 10,000 people moved into the island

So we cannot compute population density without area.

👉 Conclusion: Question 1 cannot be answered as written — missing data (area).

But perhaps the question meant to ask something else? Let’s look at the context.

Wait — maybe the "current population" already includes the migration? Let's see.

The problem says:
> "There are currently 250,000 inhabitants of the island."

And:
> "Last year, there were 12,000 new children born and 10,000 people who moved into the island."

This suggests that the current population of 250,000 already includes those who were born and migrated last year.

But still no area.

So unless the area was included in the image but not copied here, we can’t calculate density.

But perhaps the question is asking for population change or rate, not density?

Wait — let's re-read:

> 1. What is the current population density?

→ Still needs area.

Possibility: Maybe the area was shown in the image, but not in the text.

Since I can't see the image, I’ll assume that the area is missing.

But let’s proceed to Question 2, which can be answered.

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✔ Question 2: What are the birth and death rates?

We are given:
- Number of births = 12,000
- Population = 250,000
- Deaths = Not given

Wait — death rate is not provided.

We are told:
- 12,000 births
- 10,000 people moved in (immigration)
- But no number of deaths or emigration

So we cannot compute death rate unless we assume something.

But again — maybe the death rate is missing.

Wait — perhaps the problem is incomplete?

Let me check again.

The only numbers given:
- Population: 250,000
- Births: 12,000
- Immigration: 10,000
- No deaths
- No emigration

So we cannot compute death rate.

But maybe the question is asking for birth rate only?

Let’s try calculating birth rate:

$$
\text{Birth Rate} = \left( \frac{12,000}{250,000} \right) \times 1000 = 48 \text{ births per 1,000 people per year}
$$

So:
- Birth Rate = 48‰ (per thousand)

But death rate cannot be calculated because no death data is given.

So unless the image had additional info (like 8,000 deaths), we can't do it.

But wait — maybe "moved into" implies immigration, but no emigration mentioned.

Still — no death count.

So unless the death rate is zero, which is unlikely, we can't compute it.

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Possible Interpretation:

Maybe the current population of 250,000 is after births and immigration, so we can compute natural increase or net migration, but still not death rate.

Alternatively, perhaps the problem assumes that death rate is zero? Unlikely.

Wait — maybe the image showed a death count, but it's missing from the text.

Given that, I suspect the original image included:
- Deaths = 8,000 (common in such problems)

But since it's not here, I’ll assume the data is incomplete.

But let’s suppose deaths are not given, so we can only compute birth rate.

So:

✔ Answer to Question 2 (partial):

- Birth Rate = $ \frac{12,000}{250,000} \times 1000 = 48 $ per 1,000
- Death Rate = Not enough information (no deaths given)

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But wait — perhaps the question is asking for birth rate and death rate, but only birth is possible.

Alternatively, maybe the "moved into" is not relevant for birth/death rates.

Yes — birth and death rates are crude rates, based on births and deaths per population.

So:
- Birth Rate = $ \frac{12,000}{250,000} \times 1000 = 48 $ ‰
- Death Rate = ???

So unless deaths are given, we can't find it.

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Conclusion:

The problem is missing key data:
- Area (for density)
- Number of deaths (for death rate)

But perhaps in the image, those were provided.

Let me try to reconstruct what might be intended.

Suppose:
- Area = 50,000 sq km (example)
- Deaths = 8,000

Then:
1. Density = $ \frac{250,000}{50,000} = 5 $ people per sq km
2. Birth Rate = $ \frac{12,000}{250,000} \times 1000 = 48 $ ‰
Death Rate = $ \frac{8,000}{250,000} \times 1000 = 32 $ ‰

But since no such values are in the text, I can't assume.

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Best I Can Do Without Image:

Let’s assume that the only data given is what’s in the text.

So:

#### Answer to Question 1:
- Cannot be determined — area not provided

#### Answer to Question 2:
- Birth Rate = $ \frac{12,000}{250,000} \times 1000 = 48 $ per 1,000
- Death Rate = Insufficient data (no death count given)

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But wait — perhaps the "moved into" is not part of the population calculation for birth/death rates — it’s just net migration.

So birth and death rates are independent of migration.

So only birth rate can be computed.

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Final Answer (based on available data):

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1. What is the current population density?
✘ Cannot be determined — area of the island is not provided.

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2. What are the birth and death rates?
✔ Birth Rate = $ \frac{12,000}{250,000} \times 1000 = 48 $ per 1,000 people per year
✘ Death Rate = Cannot be determined — number of deaths not provided.

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If you can provide the area and/or number of deaths from the image, I can update the solution.

Alternatively, if the image showed:
- Area = 100,000 sq km
- Deaths = 9,000

Then:
- Density = $ \frac{250,000}{100,000} = 2.5 $ people/sq km
- Death Rate = $ \frac{9,000}{250,000} \times 1000 = 36 $ ‰

But until then, this is the best I can do.

Please confirm if there’s more data in the image.