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:
Where:
- represents the population.
- is the number of years after 2018.
- is Euler's number (approximately 2.71828).
- The population starts at 100,000 in the year 2018.
To calculate the expected population in 2023:
-
First, calculate , the number of years since 2018:
-
Now, substitute into the population formula:
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:
- How would the population change if the growth rate were higher, say 0.01?
- What would be the population in 2030, assuming the same growth rate?
- How can we calculate the growth rate if given two population figures?
- What is the doubling time for the population with this growth rate?
- 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