Question
A wildlife manager determines there are approximately 200 deer in a certain state park. The population is growing at a rate of 7% per year.
Which exponential equation models this situation?
(1 point)
Responses
y=200+1.07xy is equal to 200 plus 1 point 0 7 x
y=200(1.07)xy is equal to 200 times 1 point 0 7 to the x th power
y=200(0.93)xy is equal to 200 times 0 point 9 3 to the x th power
y=200(0.07)xy is equal to 200 times 0 point 0 7 to the x th power
Question 2
A wildlife manager determines there are approximately 200 deer in a certain state park. The population is growing at a rate of 7% per year.(1 point)
How many deer will live in the park after 4 years? Round to the nearest whole deer. Type your answer HERE. >>>
Which exponential equation models this situation?
(1 point)
Responses
y=200+1.07xy is equal to 200 plus 1 point 0 7 x
y=200(1.07)xy is equal to 200 times 1 point 0 7 to the x th power
y=200(0.93)xy is equal to 200 times 0 point 9 3 to the x th power
y=200(0.07)xy is equal to 200 times 0 point 0 7 to the x th power
Question 2
A wildlife manager determines there are approximately 200 deer in a certain state park. The population is growing at a rate of 7% per year.(1 point)
How many deer will live in the park after 4 years? Round to the nearest whole deer. Type your answer HERE. >>>
Answers
GPT-4o mini
To model the growth of the deer population, we can use the exponential growth formula:
\[ y = a(1 + r)^x \]
where:
- \( y \) is the future population,
- \( a \) is the initial population (200 deer),
- \( r \) is the growth rate (0.07 for 7%), and
- \( x \) is the number of years.
So the correct exponential equation that models this situation is:
**y = 200(1.07)^x**
---
**Question 2:**
We need to find the population after 4 years using the equation we identified:
\[ y = 200(1.07)^4 \]
Calculating that:
1. Calculate \( 1.07^4 \):
\[ 1.07^4 \approx 1.3107961 \]
2. Multiply by 200:
\[ y \approx 200 \times 1.3107961 \approx 262.15922 \]
Rounding to the nearest whole deer, the population after 4 years will be approximately **262 deer**.
\[ y = a(1 + r)^x \]
where:
- \( y \) is the future population,
- \( a \) is the initial population (200 deer),
- \( r \) is the growth rate (0.07 for 7%), and
- \( x \) is the number of years.
So the correct exponential equation that models this situation is:
**y = 200(1.07)^x**
---
**Question 2:**
We need to find the population after 4 years using the equation we identified:
\[ y = 200(1.07)^4 \]
Calculating that:
1. Calculate \( 1.07^4 \):
\[ 1.07^4 \approx 1.3107961 \]
2. Multiply by 200:
\[ y \approx 200 \times 1.3107961 \approx 262.15922 \]
Rounding to the nearest whole deer, the population after 4 years will be approximately **262 deer**.