Math Problem Statement

Solve

What is the expected population of the town in 2023, given the exponential growth formula P = 100000 * e^(0.007t), where t represents the number of years after 2018?

Solution

The problem shows the following exponential population growth formula:

P=100000e0.007tP = 100000 \cdot e^{0.007t}

Where:

  • PP represents the population.
  • tt is the number of years after 2018.
  • ee is Euler's number (approximately 2.71828).
  • The population starts at 100,000 in the year 2018.

To calculate the expected population in 2023:

  1. First, calculate tt, the number of years since 2018: t=20232018=5t = 2023 - 2018 = 5

  2. Now, substitute t=5t = 5 into the population formula: P=100000e0.007×5P = 100000 \cdot e^{0.007 \times 5}

I'll now compute this value.The expected population in 2023 is approximately 103,562.

Would you like more details on this calculation or have any further questions?

Here are 5 related questions you might explore:

  1. How would the population change if the growth rate were higher, say 0.01?
  2. What would be the population in 2030, assuming the same growth rate?
  3. How can we calculate the growth rate if given two population figures?
  4. What is the doubling time for the population with this growth rate?
  5. How does exponential growth differ from linear growth in terms of long-term population trends?

Tip: In exponential growth, small increases in the growth rate can lead to significantly larger populations over time.

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Math Problem Analysis

Mathematical Concepts

Exponential Growth
Algebra
Population Modeling

Formulas

P = 100000 * e^(0.007t)

Theorems

Exponential Growth Theorem

Suitable Grade Level

Grades 9-12