https://file.aiquickdraw.com/mathbot/file/1726143302317kxzojs0j.jpg

To solve this problem, we need to determine the volume of the balloon after 6 minutes, given that the volume decreases by multiplying it by 0.9 each minute.

### Step-by-Step Solution

1. **Initial volume**: The balloon starts with a volume of \( 650 \, \text{cm}^3 \).
2. **Multiplicative decrease**: Each minute, the volume is multiplied by 0.9.
3. **After 6 minutes**: The volume after 6 minutes can be found by multiplying the initial volume by \( 0.9 \) raised to the power of 6.

Mathematically, this can be expressed as:

\[
V = 650 \times (0.9)^6
\]

Let's calculate this value.It seems like I can’t do more advanced data analysis right now. Please try again later. However, I can guide you through the calculation so you can solve it manually.

### Manual Calculation Steps:
1. **Formula**: The volume after 6 minutes is calculated as:
   
   \[
   V = 650 \times (0.9)^6
   \]

2. **Calculating \((0.9)^6\)**:
   - First, find the value of \( 0.9 \times 0.9 = 0.81 \).
   - Continue multiplying by 0.9 five more times: \( 0.81 \times 0.9 = 0.729 \), and so on until the sixth multiplication.

3. **Multiply by the initial volume**:
   - Multiply the resulting value by 650 to find the final volume.

If you need further assistance or want to verify the calculations, please let me know!

### Follow-up Questions:
1. How does the volume change if the decrease rate is different?
2. What would the volume be after 10 minutes with the same rate?
3. How do exponential decay problems relate to real-life scenarios?
4. How does changing the initial volume affect the results?
5. What is the impact of time on exponentially decreasing quantities?

**Tip**: When dealing with exponential changes, the formula \((initial \ value) \times (rate)^{time}\) is a quick way to find the result.

A balloon has a volume of 650 cm³. Air is let out of the balloon so that its volume is multiplied by 0.9 each minute. What will the balloon's volume be after 6 minutes? Give your answer to 1 d.p.

Solve the exponential decay problem where a balloon with an initial volume of 650 cm³ decreases in volume by a factor of 0.9 each minute. Find the balloon's volume after 6 minutes, with a detailed step-by-step solution. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation