The population of a city grows at a rate of 2,000 people per year. If the population is initially 100,000 people, which of the following equations represents the population (P) in terms of the number of years (t)?


Question 6Answer

a.

P = 2,000t + 100,000 


b.

P = 2,000t - 100,000 


c.

P = 100,000t + 2,000 


d.

P = 100,000t - 2,000

The population grows at a constant rate of 2,000 people per year, and the initial population is 100,000 people. This type of problem represents a linear relationship, where the rate of growth (slope) is 2,000, and the initial population (y-intercept) is 100,000.

The general form of a linear equation is:

\[
P(t) = \text{rate} \times t + \text{initial population}
\]

Substituting the given values:

\[
P(t) = 2000t + 100,000
\]

Thus, the correct equation is:

**a. \( P = 2,000t + 100,000 \)**

Would you like further details on this? Here are some related questions to extend your understanding:

1. How would the equation change if the growth rate increased to 3,000 people per year?
2. What if the population started at 120,000 people instead of 100,000?
3. How would you graph the population over time using this equation?
4. What is the population after 5 years according to this model?
5. How does this equation compare to exponential growth models?

**Tip:** In linear models like this, the population grows by the same amount each year, which is why we use the slope-intercept form for the equation.

The population of a city grows at a rate of 2,000 people per year. If the population is initially 100,000 people, which of the following equations represents the population (P) in terms of the number of years (t)?

Understand how to represent the population growth of a city using a linear equation. The city's population increases by 2,000 people annually, starting from 100,000. Learn how to derive and use the equation P = 2,000t + 100,000. This example demonstrates key algebra concepts and is suitable for Grades 6-8.

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