In January 2005, the population of California was 36.8 million and growing at an annual rate of 1.3%. Assume that growth continues at the same rate. By how much will the population increase between 2025 and 2045?
By _____ million (to the nearest 0.001 million)

To find the population increase between 2025 and 2045, we can model the population growth using the formula for exponential growth:

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

where:
- \( P(t) \) is the population at time \( t \) years after the initial population,
- \( P_0 \) is the initial population (36.8 million in 2005),
- \( r \) is the growth rate (1.3% = 0.013),
- \( t \) is the number of years after 2005.

### Step 1: Calculate the population in 2025
The number of years between 2005 and 2025 is \( t = 2025 - 2005 = 20 \). Using the formula:

\[
P(2025) = 36.8 \times (1 + 0.013)^{20}
\]

### Step 2: Calculate the population in 2045
The number of years between 2005 and 2045 is \( t = 2045 - 2005 = 40 \). Using the same formula:

\[
P(2045) = 36.8 \times (1 + 0.013)^{40}
\]

### Step 3: Calculate the increase in population between 2025 and 2045
The population increase is the difference:

\[
\Delta P = P(2045) - P(2025)
\]

Let me compute this.The population of California is projected to increase by approximately **14.044 million** between 2025 and 2045, assuming the growth rate remains at 1.3%.

Do you want further details or have any questions?

Here are 5 related questions to expand on this topic:
1. How would the result change if the growth rate was 1.5% instead of 1.3%?
2. What would be the population in 2060 assuming the same growth rate?
3. How do you derive the exponential growth formula used here?
4. What is the difference between exponential and linear growth models?
5. How would a decrease in the growth rate affect long-term population projections?

**Tip:** When working with exponential growth, small changes in the growth rate can have significant effects over long time periods.

In January 2005, the population of California was 36.8 million and growing at an annual rate of 1.3%. Assume that growth continues at the same rate. By how much will the population increase between 2025 and 2045? By _____ million (to the nearest 0.001 million).

Learn how to calculate the population increase in California between 2025 and 2045 using exponential growth. The population grows at 1.3% annually. This problem covers key concepts like exponential growth formulas and population modeling. Suitable for Grades 10-12 students.

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