The population of a big city is increasing at a rate of 2.5% per year. The city’s current population is 67,000. Make a table and graph 

To model the population growth of the city, we can use the formula for exponential growth:

\[
P(t) = P_0 \cdot (1 + r)^t
\]

Where:
- \( P(t) \) is the population at time \( t \) (in years),
- \( P_0 \) is the initial population (67,000),
- \( r \) is the growth rate (2.5% per year, which is 0.025 in decimal form),
- \( t \) is the number of years.

### Table: Population Growth Over Time

Let’s calculate the population for the next few years, say 0 to 10 years, using the formula.

| Year (\( t \)) | Population (\( P(t) \)) |
|----------------|-------------------------|
| 0              | 67,000                  |
| 1              | \( 67,000 \cdot (1 + 0.025)^1 = 68,675 \) |
| 2              | \( 67,000 \cdot (1 + 0.025)^2 = 70,392 \) |
| 3              | \( 67,000 \cdot (1 + 0.025)^3 = 72,152 \) |
| 4              | \( 67,000 \cdot (1 + 0.025)^4 = 73,956 \) |
| 5              | \( 67,000 \cdot (1 + 0.025)^5 = 75,805 \) |
| 6              | \( 67,000 \cdot (1 + 0.025)^6 = 77,700 \) |
| 7              | \( 67,000 \cdot (1 + 0.025)^7 = 79,642 \) |
| 8              | \( 67,000 \cdot (1 + 0.025)^8 = 81,633 \) |
| 9              | \( 67,000 \cdot (1 + 0.025)^9 = 83,674 \) |
| 10             | \( 67,000 \cdot (1 + 0.025)^10 = 85,766 \) |

Now, I will plot a graph showing the population growth over the 10-year period.

Let me calculate and create the graph for you.Here is the graph showing the city's population growth over a 10-year period, based on an annual increase of 2.5%.

Would you like to go into more detail about any aspect of the calculations or graph? 

Here are 5 related questions:
1. What will the population be after 15 years?
2. How long will it take for the population to double?
3. Can we model the population with continuous growth rather than annual growth?
4. How does this exponential growth differ from linear growth?
5. What would happen to the population if the growth rate increased to 3%?

**Tip:** Exponential growth is a key feature in finance, biology, and urban planning, making it a powerful tool for predicting trends over time.

The population of a big city is increasing at a rate of 2.5% per year. The city’s current population is 67,000. Make a table and graph.

Discover how to calculate and model the population growth of a city with an initial population of 67,000 and an annual growth rate of 2.5%. Learn to create a table and graph using the exponential growth formula over a 10-year period. Ideal for students in Grades 9-12.

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