Math Problem Statement
A population grows according to an exponential growth model. The initial population is 202 and the population after one year is 295. Complete the formula where P is the population and n is the number of years.: P=202*(__)^n Round your answer to three decimal places.
Solution
To determine the base of the exponential growth model, we can use the following information:
- The initial population is 202.
- After one year, the population is 295.
The exponential growth formula is: where is the growth factor per year, and is the number of years.
Since we know when , we can set up the equation:
Solving for : Calculating this value and rounding to three decimal places:
So the completed formula is:
Would you like additional details or have any questions?
Further Questions
- How does this exponential growth model change if the growth rate decreases over time?
- What would the population be after 5 years using this model?
- How would you interpret the growth factor in terms of annual growth rate?
- What other models besides exponential could represent population growth?
- How does exponential growth differ from linear growth?
Tip:
When interpreting exponential growth, a growth factor greater than 1 indicates an increase, while a factor less than 1 indicates a decrease over time.
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Math Problem Analysis
Mathematical Concepts
Exponential Growth
Algebra
Formulas
Exponential growth formula: P = P0 * r^n
Theorems
-
Suitable Grade Level
Grades 9-11
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