Questions: Question 14 1 pts Over the past ten years Vancouver, WA has grown at an average annual rate of 1.1% per year. Currently the population of Vancouver is approximately 198,000 people. If Vancouver continues to grow at this rate going forward, what would you predict the population to be in 20 years? (Hint: Use the Exponential Growth Formula) Round your answer to the nearest whole person.

Solution Steps

To solve this problem, we will use the Exponential Growth Formula, which is given by:

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

where:

• \( P(t) \) is the future population.
• \( P_0 \) is the current population.
• \( r \) is the growth rate.
• \( t \) is the number of years in the future.

Given:

• Current population \( P_0 = 198,000 \)
• Growth rate \( r = 1.1\% = 0.011 \)
• Time \( t = 20 \) years

We will plug these values into the formula to find the future population.

We start with the following values:

• Current population \( P_0 = 198,000 \)
• Growth rate \( r = 0.011 \)
• Time period \( t = 20 \)

We use the Exponential Growth Formula:

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

Substituting the known values:

\[ P(20) = 198000 \times (1 + 0.011)^{20} \]

Calculating the expression:

\[ P(20) = 198000 \times (1.011)^{20} \]

Calculating \( (1.011)^{20} \):

\[ (1.011)^{20} \approx 1.246427 \]

Now, substituting back:

\[ P(20) \approx 198000 \times 1.246427 \approx 246427.0068711241 \]

Rounding the future population to the nearest whole person gives:

\[ P(20) \approx 246427 \]

Final Answer