2 Which situation can be modeled by a linear function?
(1) A printer can print one page every three seconds.
(2) A bank account earns interest each year, compounded
annually.
The number of cells in an organism doubles every four days.
(4) The attendance at a professional sports team’s games decreases
by each year.

Question

2 Which situation can be modeled by a linear function?
(1) A printer can print one page every three seconds.
(2) A bank account earns

interest each year, compounded
annually.
The number of cells in an organism doubles every four days.
(4) The attendance at a professional sports team’s games decreases
by

each year.

UpStudy AI · Accepted Answer

To determine which situation can be modeled by a **linear function**, let's analyze each option:

1. **A printer can print one page every three seconds.**
   - **Analysis:** 
     - If $$ x $$ represents time in seconds and $$ y $$ represents the number of pages printed, the relationship is linear.
     - **Function:** $$ y = \frac{1}{3}x $$
   - **Conclusion:** **Linear**

2. **A bank account earns $$ 0.5\% $$ interest each year, compounded annually.**
   - **Analysis:** 
     - Compounded interest grows exponentially, not linearly.
     - **Function:** $$ y = P \left(1 + 0.005\right)^x $$ where $$ P $$ is the principal.
   - **Conclusion:** **Exponential, not linear**

3. **The number of cells in an organism doubles every four days.**
   - **Analysis:** 
     - This represents exponential growth.
     - **Function:** $$ y = y_0 \cdot 2^{x/4} $$
   - **Conclusion:** **Exponential, not linear**

4. **The attendance at a professional sports team's games decreases by $$ 1.5\% $$ each year.**
   - **Analysis:** 
     - This represents exponential decay.
     - **Function:** $$ y = y_0 \cdot (1 - 0.015)^x $$
   - **Conclusion:** **Exponential, not linear**

**Summary:** Only **situation (1)** can be accurately modeled using a linear function.

**Answer:** Only situation 1 can be represented by a linear function.
Only situation (1) can be modeled by a linear function.

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