Lin counts 5 bacteria under a microscope. She counts them again each day for four days, and finds that the number of bacteria doubled each day—from 5 to 10, then from 10 to 20, and so on. Which statement is true?

The graph that represents this relationship are points in a straight line.

The relationship is a linear function.

The relationship is a function but is not linear.

The relationship is not a function.

Given the situation where the number of bacteria doubles each day, we can analyze the nature of this relationship.

Let's denote:
- \( N \) as the number of bacteria
- \( t \) as the number of days

Initially, at \( t = 0 \), \( N = 5 \).
After 1 day, \( N = 10 \).
After 2 days, \( N = 20 \).
After 3 days, \( N = 40 \).
After 4 days, \( N = 80 \).

The number of bacteria follows the pattern \( N = 5 \cdot 2^t \).

To determine which statement is true, we need to analyze the characteristics of the function \( N = 5 \cdot 2^t \).

1. **The graph that represents this relationship are points in a straight line.**
   - This statement is false. An exponential function like \( N = 5 \cdot 2^t \) will produce a curve, not a straight line.

2. **The relationship is a linear function.**
   - This statement is false. A linear function has the form \( N = mt + c \), where \( m \) and \( c \) are constants. \( N = 5 \cdot 2^t \) is exponential, not linear.

3. **The relationship is a function but is not linear.**
   - This statement is true. The relationship \( N = 5 \cdot 2^t \) is a function (each input \( t \) has a unique output \( N \)), but it is exponential, not linear.

4. **The relationship is not a function.**
   - This statement is false. The relationship is indeed a function because each input \( t \) corresponds to exactly one output \( N \).

Thus, the correct statement is:

**The relationship is a function but is not linear.**

Would you like details or have any questions?

Here are 5 more math-related questions you might be interested in:

1. What are the properties of exponential functions?
2. How do you differentiate between linear and exponential growth?
3. Can you graph an exponential function and explain its features?
4. How do you solve exponential equations?
5. What is the importance of understanding exponential growth in real-world contexts?

**Tip:** Recognizing the type of function (linear, exponential, quadratic, etc.) helps in predicting and understanding the behavior of the relationship being studied.

Explore the exponential growth of bacteria as Lin counts 5 bacteria under a microscope each day for four days. Understand the relationship N = 5 * 2^t and its implications in biological and mathematical contexts. Suitable for high school students studying exponential functions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation