Math Problem Statement
A biologist studying a population of geckos for several years found that the population can be modeled as shown below, where P** is the population, and t** is the time in years.
P=230(1.04)t
What is the growth rate of this population?
Responses
4%
4 %
6%
6 %
Solution
The population growth model provided is:
This model is in the form of exponential growth, which can be written as:
Where:
- is the initial population,
- is the growth rate,
- is the time in years.
Here, , meaning that the growth rate is 0.04 or 4%.
So, the growth rate of this population is 4%.
Would you like a detailed explanation of exponential growth, or do you have any other questions?
Here are some related questions:
- How do you calculate the population at any given year using this model?
- What happens to the population if the growth rate increases to 6%?
- How can we determine the doubling time for this population?
- What is the significance of exponential growth in biological populations?
- How would you modify the equation if the population decreases by 4% annually?
Tip: In exponential growth models, the base of the exponential term (1 + r) directly represents the growth factor.
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Math Problem Analysis
Mathematical Concepts
Exponential Growth
Algebra
Formulas
Exponential growth model: P = P0(1 + r)^t
Theorems
Exponential growth theorem
Suitable Grade Level
Grades 9-12
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