Math Problem Statement
A population grows according to an exponential growth model. The initial population is Po=4 , and the growth rate is r=0.4
Solution
The population grows according to the exponential growth model, which is typically given by the formula:
Where:
- is the population at time ,
- is the initial population,
- is the growth rate (per unit time),
- is the time that has passed,
- is Euler's number (approximately 2.71828).
Given the initial population and the growth rate , the population at any time is modeled by the equation:
Example: Population after 5 years
If you want to calculate the population after 5 years, substitute into the equation:
So, after 5 years, the population would be approximately 29.56.
Would you like to calculate the population for a specific time or explore related details?
5 Related Questions:
- What will the population be after 10 years?
- How long will it take for the population to double?
- Can you solve for the time when the population reaches 100?
- How does changing the growth rate affect the population over time?
- What would happen to the population if it started at a different value of ?
Tip:
When solving exponential growth problems, it's helpful to memorize the doubling time formula: .
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Math Problem Analysis
Mathematical Concepts
Exponential Growth
Population Growth Models
Formulas
P(t) = P_0 * e^(rt)
Doubling Time Formula: T_double = ln(2)/r
Theorems
Exponential Growth Theorem
Suitable Grade Level
Grades 10-12
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