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:
The rate of growth per year is:
Step 2: Predict the population in 2030.
From 2010 to 2030, the time span is 20 years. So, the population increase would be:
Step 3: Calculate the population in 2030.
Add this increase to the population in 2010:
Therefore, the predicted population in 2030 is 320 thousand.
Would you like further details or have any questions?
Here are some related questions:
- How would this model change if population growth was exponential instead of linear?
- What if the population growth rate doubled after 2010?
- How would you adjust predictions if migration significantly impacted the population?
- Can you determine the population in any given year based on this model?
- 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