Math Problem Statement

A city has population of 200 thousand in the year 2000 , and it has a population of 240 thousand in 2010 . Predict how many thousands its population will be in 2030

Solution

To predict the population in 2030, we can assume the population growth follows a linear trend. We are given the population in the year 2000 (200 thousand) and in 2010 (240 thousand).

Step 1: Calculate the rate of population growth.

The population increased by:

240200=40 thousand over 10 years.240 - 200 = 40 \text{ thousand over 10 years}.

The rate of growth per year is:

4010=4 thousand per year.\frac{40}{10} = 4 \text{ thousand per year}.

Step 2: Predict the population in 2030.

From 2010 to 2030, the time span is 20 years. So, the population increase would be:

4×20=80 thousand.4 \times 20 = 80 \text{ thousand}.

Step 3: Calculate the population in 2030.

Add this increase to the population in 2010:

240+80=320 thousand.240 + 80 = 320 \text{ thousand}.

Therefore, the predicted population in 2030 is 320 thousand.

Would you like further details or have any questions?

Here are some related questions:

  1. How would this model change if population growth was exponential instead of linear?
  2. What if the population growth rate doubled after 2010?
  3. How would you adjust predictions if migration significantly impacted the population?
  4. Can you determine the population in any given year based on this model?
  5. How accurate is linear modeling for long-term population predictions?

Tip: Linear models assume a constant rate of change, but real-world growth may vary over time. Consider checking the nature of the growth before applying this model.

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Math Problem Analysis

Mathematical Concepts

Linear Growth
Algebra
Population Modeling

Formulas

Population Growth = Rate of Growth × Time
Rate of Growth = (Population Change) / (Time)

Theorems

Linear Growth Assumption

Suitable Grade Level

Grades 9-11