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.

Question

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. >>>

Answer 1

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.