A wildlife manager determines there are approximately 78 foxes in a certain state park. The population is growing at a rate of 3% per year.

Question

Which exponential equation models this situation?

(1 point)
Responses

y=78(0.03)x
y is equal to 78 times 0 point 0 3 to the x th power

y=78(1.03)x
y is equal to 78 times 1 point 0 3 to the x th power

y=78(0.97)x
y is equal to 78 times 0 point 9 7 to the x th power

y=78+1.03x
y is equal to 78 plus 1 point 0 3 x
Question 2
Use the equation you selected above to complete the following statement. Round your answer to the nearest whole fox. (1 point)
After 8 years, there will be
foxes in the park.

Answer 1

The correct exponential equation that models the situation of the fox population growing at a rate of 3% per year is:

y = 78(1.03)^x
(y is equal to 78 times 1.03 to the x-th power)

Now, to complete the statement for how many foxes will be in the park after 8 years, we can use the equation:

\[ y = 78(1.03)^8 \]

Calculating this:

1. Calculate \(1.03^8\): \[ 1.03^8 \approx 1.26677 \]

2. Now multiply it by 78: \[ y \approx 78 \times 1.26677 \approx 98.86 \]

Rounding to the nearest whole number gives:

After 8 years, there will be approximately 99 foxes in the park.