Question

A rare species of bird was discovered in Iowa. To protect the species, environmentalists declared the bird endangered and transplanted the birds to a protected area. The population of birds x months after being transplanted is given by B(x) = (-10x + 7) / (-2x + 3). Find lim B(x).

A) 0
B) 7/3
C) Infinity
D) 5
E) 1

Answer 1

The limit of the population of birds x months after being transplanted can be found using L'Hôpital's Rule and taking the derivative of the numerator and denominator of the function. The limit is 5.

Step-by-step explanation:

The question asks us to find the limit, lim B(x), of the population of birds x months after being transplanted. The function given is B(x) = (-10x + 7) / (-2x + 3).

To find the limit, we need to determine what happens to the function as x approaches a certain value, in this case, as x approaches infinity. We can do this by examining the behavior of the function as x becomes larger and larger.

As x approaches infinity, both the numerator and denominator of B(x) approach negative infinity. Therefore, we can apply L'Hôpital's Rule and take the derivative of the numerator and denominator to find the limit.

Taking the derivative of the numerator and denominator, we get B'(x) = -10 / -2 = 5.

Therefore, the limit of B(x) as x approaches infinity is 5, which corresponds to answer choice D) 5.