Tony's Story Tony was 85 centimeters tall on his second birthday. He grew at a steady rate until he was 10 years old. On his tenth birthday, he was 135 centimeters tall.

Question

UpStudy AI · Accepted Answer

Let's analyze Tony's growth based on the information provided.

### Given:
- **Age 2:** 85 centimeters tall
- **Age 10:** 135 centimeters tall
- **Growth Period:** From age 2 to age 10

### Objective:
Determine the **steady annual growth rate** of Tony between his second and tenth birthdays.

### Steps to Calculate the Annual Growth Rate:

1. **Calculate the Total Growth:**
   $$
   \text{Total Growth} = \text{Height at Age 10} - \text{Height at Age 2} = 135\,\text{cm} - 85\,\text{cm} = 50\,\text{cm}
   $$

2. **Determine the Number of Years Over Which the Growth Occurred:**
   $$
   \text{Number of Years} = 10\,\text{years} - 2\,\text{years} = 8\,\text{years}
   $$

3. **Calculate the Annual Growth Rate:**
   $$
   \text{Annual Growth Rate} = \frac{\text{Total Growth}}{\text{Number of Years}} = \frac{50\,\text{cm}}{8\,\text{years}} = 6.25\,\text{cm/year}
   $$

### Conclusion:
Tony grew at a **steady rate of 6.25 centimeters per year** between his second and tenth birthdays.

### Additional Insights:
- **Height at Any Given Age (Between 2 and 10):**
  You can model Tony's height $$ H $$ at any age $$ a $$ between 2 and 10 years using the linear equation:
  $$
  H(a) = 85\,\text{cm} + 6.25\,\text{cm/year} \times (a - 2)
  $$
  
  **Example:**  
  To find Tony's height at age 5:
  $$
  H(5) = 85\,\text{cm} + 6.25\,\text{cm/year} \times (5 - 2) = 85\,\text{cm} + 18.75\,\text{cm} = 103.75\,\text{cm}
  $$

This linear model assumes that Tony's growth rate remained constant at 6.25 cm/year during the specified age range.
Tony grew at a steady rate of 6.25 centimeters each year from age 2 to 10.

Tony’s Story
Tony was 85 centimeters tall on his second birthday. He
grew at a steady rate until he was 10 years old. On his
tenth birthday, he was 135 centimeters tall.

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Tony’s Story Tony was 85 centimeters tall on his second birthday. He grew at a steady rate until he was 10 years old. On his tenth birthday, he was 135 centimeters tall.