Math Problem Statement

The population of a village was 10,000 one year ago. The population at present is 10,210; find the population growth rate.

Solution

From the image provided, the questions seem to deal with population growth or decay, requiring the calculation of growth or decreasing rates over time. Let's address the mathematical problem-solving approach.

For example, let's break down Question 8A:

The problem states:

  • Population 1 year ago: 10,000
  • Current population: 10,210
  • Find the population growth rate.

Solution:

The formula for the growth rate (rr) is: r=Change in PopulationInitial Population×100r = \frac{\text{Change in Population}}{\text{Initial Population}} \times 100

  1. Change in Population = 10,21010,000=21010,210 - 10,000 = 210
  2. Growth Rate: r=21010,000×100=2.1%r = \frac{210}{10,000} \times 100 = 2.1\%

The population growth rate is 2.1%.


Let me know which question you'd like to solve next, or if you'd like detailed explanations for others.


Further Exploration:

Here are related questions to expand your understanding:

  1. What formula would you use for population decrease rates, as in Question 8B?
  2. How can you calculate the growth rate over multiple years?
  3. What assumptions are we making about the growth in these problems?
  4. How would a negative rate impact future populations?
  5. Can you write a formula for predicting future populations using the growth rate?

Tip: Always double-check population changes and initial values to avoid calculation errors.

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Math Problem Analysis

Mathematical Concepts

Population Growth
Percentage Calculation
Arithmetic

Formulas

Growth Rate = (Change in Population / Initial Population) × 100

Theorems

Proportional Change Theorem

Suitable Grade Level

Grade 8-10