Math Problem Statement
The fox population in a certain region has an annual growth rate of 6 percent per year. It is estimated that the population in the year 2000 was 26000. (a) Find a function that models the population t years after 2000 (t= 0 for 2000). Your answer is p(t)=
Solution
To model the population of foxes over time, we can use an exponential growth formula:
Where:
- is the population at time ,
- is the initial population (in the year 2000),
- is the annual growth rate,
- is the time in years after the year 2000.
Given:
- ,
- .
Thus, the population function becomes:
So the function that models the population years after 2000 is:
Would you like further details or have any questions?
Here are 5 related questions:
- What will the fox population be in the year 2010?
- How long will it take for the fox population to double?
- What is the population growth over the first 5 years?
- How does this model change if the growth rate decreases to 4%?
- What assumptions does this exponential model rely on?
Tip: Exponential growth models assume unlimited resources, which may not always be realistic in ecological scenarios!
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Math Problem Analysis
Mathematical Concepts
Exponential Growth
Population Modeling
Formulas
P(t) = P_0 * (1 + r)^t
Theorems
Exponential Growth Model
Suitable Grade Level
Grades 10-12
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