The population​ (in thousands) of people of a city is approximated by the function Upper P left parenthesis t right parenthesis equals 1100 left parenthesis 2 right parenthesis Superscript 0.1027 tP(t)=1100(2)0.1027t​, where t is the number of years since 20112011.
a. Find the population of this group in 20182018.
b. Predict the population in 20262026.

We are given the population function:

\[
P(t) = 1100 \times 2^{0.1027t}
\]

Where:
- \( t \) is the number of years since 2011.
- \( P(t) \) is the population in thousands.

### Part (a): Find the population in 2018

To find the population in 2018, we first determine the value of \( t \) for 2018:

\[
t = 2018 - 2011 = 7
\]

Now substitute \( t = 7 \) into the population formula:

\[
P(7) = 1100 \times 2^{0.1027 \times 7}
\]

### Part (b): Predict the population in 2026

Similarly, to find the population in 2026, calculate \( t \) for 2026:

\[
t = 2026 - 2011 = 15
\]

Now substitute \( t = 15 \) into the population formula:

\[
P(15) = 1100 \times 2^{0.1027 \times 15}
\]

Let's calculate both parts.### Results:

- **Population in 2018**: Approximately 1810.52 thousand (or 1.81 million people).
- **Predicted population in 2026**: Approximately 3199.85 thousand (or 3.20 million people).

Would you like further details on the calculations, or do you have any other questions?

Here are 5 related questions for you to consider:
1. How does the population growth rate impact long-term projections?
2. What is the doubling time for the population based on this model?
3. How would changes in the exponent factor affect population predictions?
4. Can this model be extended to predict the population in 2050? What assumptions would be needed?
5. What are the potential limitations of using an exponential model for population growth?

**Tip**: Exponential models, like this one, assume a constant growth rate, which might not always hold over long periods due to factors like resource limitations or policy changes.

The population​ (in thousands) of people of a city is approximated by the function P(t) = 1100(2)^0.1027t, where t is the number of years since 2011.
 a. Find the population of this group in 2018.
 b. Predict the population in 2026.

Learn how to predict population growth using the exponential function P(t) = 1100(2)^0.1027t. This problem involves calculating the population in 2018 and predicting it for 2026. Suitable for students in Grades 9-12.

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