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Logistic Growth - Worksheet 10 - 12th Grade

Hard

Use explicitly stated exponential and logarithmic models and interpret their parameters.

hard: Use another set to practice explaining and checking your answers.

18 problems · 25-30 minutes · Skills: exponential, modeling, functions

About This Worksheet

This hard-level worksheet contains 18 problems designed for 12th Grade students practicing logistic growth. Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.

Evaluate functions, solve for variables and use exponential/logarithmic inverses.

  • Use explicitly stated exponential and logarithmic models and interpret their parameters.
  • Check your result using the method in the example before moving to the next question.

How to Solve: Worked Example

Example Problem: A logistic model is P(t) = 300/(1 + 2e^(−t)), t ≥ 0. Find P(0).
Solution Steps:
  1. At t = 0, the exponential factor is 1.
  2. Divide K by 1 + the coefficient of the exponential.
Answer: 100
Tip: Check your result using the method in the example before moving to the next question.
1
A logistic model is P(t) = 700/(1 + 1e^(−t)), t ≥ 0. Find P(0).
2
A logistic model is P(t) = 700/(1 + 8e^(−t)), t ≥ 0. What is its carrying capacity?
3
A logistic model is P(t) = 400/(1 + 6e^(−t)), t ≥ 0. Find P(0).
4
A logistic model is P(t) = 300/(1 + 2e^(−t)), t ≥ 0. What is its carrying capacity?
5
A logistic model is P(t) = 400/(1 + 5e^(−t)), t ≥ 0. Find P(0).
6
A logistic model is P(t) = 200/(1 + 9e^(−t)), t ≥ 0. What is its carrying capacity?
7
A logistic model is P(t) = 1000/(1 + 3e^(−t)), t ≥ 0. Find P(0).
8
A logistic model is P(t) = 300/(1 + 6e^(−t)), t ≥ 0. What is its carrying capacity?
9
A logistic model is P(t) = 1000/(1 + 8e^(−t)), t ≥ 0. Find P(0).
10
A logistic model is P(t) = 1000/(1 + 1e^(−t)), t ≥ 0. What is its carrying capacity?
11
A logistic model is P(t) = 200/(1 + 4e^(−t)), t ≥ 0. Find P(0).
12
A logistic model is P(t) = 100/(1 + 8e^(−t)), t ≥ 0. What is its carrying capacity?
13
A logistic model is P(t) = 100/(1 + 7e^(−t)), t ≥ 0. Find P(0).
14
A logistic model is P(t) = 1000/(1 + 7e^(−t)), t ≥ 0. What is its carrying capacity?
15
A logistic model is P(t) = 100/(1 + 9e^(−t)), t ≥ 0. Find P(0).
16
A logistic model is P(t) = 200/(1 + 1e^(−t)), t ≥ 0. What is its carrying capacity?
17
A logistic model is P(t) = 600/(1 + 1e^(−t)), t ≥ 0. Find P(0).
18
A logistic model is P(t) = 600/(1 + 1e^(−t)), t ≥ 0. What is its carrying capacity?

Answer Key

1. 3502. 7003. 400/74. 3005. 200/36. 2007. 2508. 3009. 1000/910. 100011. 4012. 10013. 25/214. 100015. 1016. 20017. 30018. 600

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What skills does this exponential & logarithmic applications worksheet cover?

This worksheet focuses on exponential, modeling, functions. It is designed for 12th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

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How many problems are on this worksheet?

This worksheet contains 18 problems. It typically takes 25-30 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.