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The problem involves a function modeling the population in California, given by:

\[
f(t) = 3800e^{0.04t} \text{ million}
\]

Here, \( t \) represents the number of years after 1900.

The problem asks you to:
1. Use the **Discrete Decay App** to model a 10% yearly reduction in the population, and compare this with the continuous growth model given by the function \( f(t) \).
2. Utilize the app to estimate the time needed for the population to reduce to 10% of its initial value.

Would you like a detailed breakdown of these steps or further clarification on specific aspects of this problem? Let me know if you need help with understanding or solving it.

Here are some additional related questions you might consider:
1. What is the continuous growth rate in the original model?
2. How do you calculate the population after a certain number of years using the function \( f(t) \)?
3. How does a discrete decay model differ from a continuous growth model?
4. What is the significance of the 10% reduction rate in the context of population modeling?
5. How would you plot the population over time using both the continuous and discrete models?

**Tip:** When comparing models, always check the underlying assumptions, like whether they assume continuous or discrete time intervals.

The problem involves a function modeling the population in California, given by:
f(t) = 3800e^(0.04t) million

The problem asks you to:
1. Use the Discrete Decay App to model a 10% yearly reduction in the population, and compare this with the continuous growth model given by the function f(t).
2. Utilize the app to estimate the time needed for the population to reduce to 10% of its initial value.

Explore the population modeling problem in California using the function f(t) = 3800e^(0.04t) million. This problem involves comparing continuous exponential growth with a 10% yearly discrete decay model. Learn how to estimate the time needed for the population to reduce to 10% of its initial value. Suitable for students in Grades 11-12.

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