https://file.aiquickdraw.com/mathbot/file/1726084310051foxsobvk.jpg

Let's go through the details of the problem from the image you uploaded.

The problem involves modeling the growth of a zombie population using the logistic function:

\[
Z(t) = \frac{315}{1 + 14e^{-0.23t}}
\]

Where:
- \( Z(t) \) represents the population of zombies in thousands, as a function of time \( t \) (days).
- \( t \) is time in days.
- The table in part (a) gives values of \( Z \) at different days \( t \).

The tasks provided are:

1. **Part a**: Use Desmos or another graphing tool to plot the logistic function with the appropriate domain and range based on the table provided.
   - The table lists specific values of \( t \) (days) and \( Z(t) \) (zombie population) at those times.

2. **Part b**: The limiting value of the function.
   - As \( t \to \infty \), the population approaches the limiting value (which can be seen from the function).

3. **Part c**: Estimate the \( t \)-values for which the function is concave up.
   - This involves analyzing the second derivative of the logistic function to find intervals where it is concave up.

4. **Part d**: Calculate the original population of zombies at \( t = 0 \).
   - Substituting \( t = 0 \) into the logistic equation.

5. **Part e**: Estimate when the population of zombies will reach 200,000.
   - This involves solving \( Z(t) = 200 \) (since \( Z(t) \) is in thousands).

Would you like me to help you with solving each part or focus on a specific question? Let me know!



It is estimated that the nuclear fallout from the Tahlequah Nuclear Power Plant will cause a zombie outbreak. The population of zombies follows the logistic curve given by Z(t) = 315 / (1 + 14e^(-0.23t)), where Z is in thousands and t is in days. The problem involves calculating the population at different time intervals and estimating specific population milestones.

This problem involves modeling the growth of a zombie population with a logistic growth curve Z(t) = 315 / (1 + 14e^(-0.23t)), including analysis of limiting values, concavity, and estimating population milestones. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation