Question
there are 170 deer on reservation the deer population is increasing at a rate of 30% each year the tables shown the numbers of deer Y and X after years use a table answer your question 0 year=170 1 year= 221 3year=373 5year=631 10year=2344 how does the growth rate of the deer from 1 to 3 years compared to the growth rate of the deer from 5 to 10 years show your work
Answers
GPT-4o mini
To compare the growth rates of the deer population from 1 to 3 years and from 5 to 10 years, we will calculate the growth for each of these periods and then express that growth as a percentage.
### Given Data:
1. **Year 0**: 170
2. **Year 1**: 221
3. **Year 3**: 373
4. **Year 5**: 631
5. **Year 10**: 2344
### Step 1: Calculate Growth from Year 1 to Year 3
- **Population at Year 1**: 221
- **Population at Year 3**: 373
**Growth** (Year 1 to Year 3):
\[ \text{Growth} = \text{Population at Year 3} - \text{Population at Year 1} \]
\[ \text{Growth} = 373 - 221 \]
\[ \text{Growth} = 152 \]
**Growth Rate** (as a percentage):
\[ \text{Growth Rate} = \left(\frac{\text{Growth}}{\text{Population at Year 1}}\right) \times 100 \]
\[ \text{Growth Rate} = \left(\frac{152}{221}\right) \times 100 \]
\[ \text{Growth Rate} \approx 68.87\% \]
### Step 2: Calculate Growth from Year 5 to Year 10
- **Population at Year 5**: 631
- **Population at Year 10**: 2344
**Growth** (Year 5 to Year 10):
\[ \text{Growth} = \text{Population at Year 10} - \text{Population at Year 5} \]
\[ \text{Growth} = 2344 - 631 \]
\[ \text{Growth} = 1713 \]
**Growth Rate** (as a percentage):
\[ \text{Growth Rate} = \left(\frac{\text{Growth}}{\text{Population at Year 5}}\right) \times 100 \]
\[ \text{Growth Rate} = \left(\frac{1713}{631}\right) \times 100 \]
\[ \text{Growth Rate} \approx 271.63\% \]
### Summary:
- **Growth Rate from Year 1 to Year 3**: Approximately **68.87%**
- **Growth Rate from Year 5 to Year 10**: Approximately **271.63%**
### Conclusion:
The growth rate of the deer population from Year 5 to Year 10 (approximately 271.63%) is significantly higher than the growth rate from Year 1 to Year 3 (approximately 68.87%). This implies that the population is increasing at an accelerating rate in the later years.
### Given Data:
1. **Year 0**: 170
2. **Year 1**: 221
3. **Year 3**: 373
4. **Year 5**: 631
5. **Year 10**: 2344
### Step 1: Calculate Growth from Year 1 to Year 3
- **Population at Year 1**: 221
- **Population at Year 3**: 373
**Growth** (Year 1 to Year 3):
\[ \text{Growth} = \text{Population at Year 3} - \text{Population at Year 1} \]
\[ \text{Growth} = 373 - 221 \]
\[ \text{Growth} = 152 \]
**Growth Rate** (as a percentage):
\[ \text{Growth Rate} = \left(\frac{\text{Growth}}{\text{Population at Year 1}}\right) \times 100 \]
\[ \text{Growth Rate} = \left(\frac{152}{221}\right) \times 100 \]
\[ \text{Growth Rate} \approx 68.87\% \]
### Step 2: Calculate Growth from Year 5 to Year 10
- **Population at Year 5**: 631
- **Population at Year 10**: 2344
**Growth** (Year 5 to Year 10):
\[ \text{Growth} = \text{Population at Year 10} - \text{Population at Year 5} \]
\[ \text{Growth} = 2344 - 631 \]
\[ \text{Growth} = 1713 \]
**Growth Rate** (as a percentage):
\[ \text{Growth Rate} = \left(\frac{\text{Growth}}{\text{Population at Year 5}}\right) \times 100 \]
\[ \text{Growth Rate} = \left(\frac{1713}{631}\right) \times 100 \]
\[ \text{Growth Rate} \approx 271.63\% \]
### Summary:
- **Growth Rate from Year 1 to Year 3**: Approximately **68.87%**
- **Growth Rate from Year 5 to Year 10**: Approximately **271.63%**
### Conclusion:
The growth rate of the deer population from Year 5 to Year 10 (approximately 271.63%) is significantly higher than the growth rate from Year 1 to Year 3 (approximately 68.87%). This implies that the population is increasing at an accelerating rate in the later years.