A population grows according to an exponential growth model. The initial population is Po=4 , and the growth rate is r=0.4

The population grows according to the exponential growth model, which is typically given by the formula:

\[
P(t) = P_0 e^{rt}
\]

Where:
- \( P(t) \) is the population at time \( t \),
- \( P_0 \) is the initial population,
- \( r \) is the growth rate (per unit time),
- \( t \) is the time that has passed,
- \( e \) is Euler's number (approximately 2.71828).

Given the initial population \( P_0 = 4 \) and the growth rate \( r = 0.4 \), the population at any time \( t \) is modeled by the equation:

\[
P(t) = 4 e^{0.4t}
\]

### Example: Population after 5 years
If you want to calculate the population after 5 years, substitute \( t = 5 \) into the equation:

\[
P(5) = 4 e^{0.4 \times 5} = 4 e^{2} \approx 4 \times 7.3891 = 29.5564
\]

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:
1. What will the population be after 10 years?
2. How long will it take for the population to double?
3. Can you solve for the time when the population reaches 100?
4. How does changing the growth rate \(r\) affect the population over time?
5. What would happen to the population if it started at a different value of \(P_0\)?

### Tip:
When solving exponential growth problems, it's helpful to memorize the doubling time formula: \( T_{\text{double}} = \frac{\ln(2)}{r} \).

A population grows according to an exponential growth model. The initial population is Po=4, and the growth rate is r=0.4.

Explore how a population grows exponentially starting from an initial population of 4 with a growth rate of 0.4. Learn the exponential growth model formula, calculate future population sizes, and understand key growth concepts. Suitable for high school students in Grades 10-12.

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