Math Problem Statement

Which of the contexts below represents exponential growth?

Solution

The question asks which of the contexts represents exponential growth. Let's analyze each of the options:

  1. The amount of certain medication in a person's bloodstream decreases by 23\frac{2}{3} every hour.

    • This represents exponential decay (not growth), as the amount of medication is decreasing over time.
  2. A population of 200 bacteria quintuples every week.

    • This is an example of exponential growth because the population increases by a factor of 5 every week, which is a characteristic of exponential growth.
  3. Snow was falling at a rate of 1.75 inches per hour.

    • This describes linear growth, not exponential growth, because the snow falls at a constant rate.
  4. A car depreciates at a rate of 5.3% per year.

    • This is exponential decay, as the car's value decreases by a fixed percentage each year.

So, the correct context representing exponential growth is "A population of 200 bacteria quintuples every week."

Would you like a more detailed explanation or have any further questions?

Here are five related questions for further exploration:

  1. How do we define exponential growth in mathematical terms?
  2. Can exponential growth ever slow down over time?
  3. What are some real-life examples of exponential growth?
  4. How do you calculate exponential growth using a formula?
  5. What is the difference between exponential growth and linear growth?

Tip: To identify exponential growth, look for situations where the quantity is multiplying by a fixed factor over time.

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Math Problem Analysis

Mathematical Concepts

Exponential Growth
Exponential Decay
Linear Growth

Formulas

Exponential Growth Formula: P(t) = P_0 * r^t

Theorems

Properties of Exponential Functions

Suitable Grade Level

Grades 8-10