Question

Suppose that 30 deer are introduced in a protected wilderness area. The population of the herd can be approximated by ()= 30+2 1+.05 , where is the time in years since introducing the deer. Write the equation of the horizontal asymptote for this function. Also, interpret what this asymptote means in the context of the problem (in terms of the deer population and the number of years since the deer were introduced into the wilderness area).

Answer 1

The horizontal asymptote of the function is the minimum number of deer in the area.

• The equation of horizontal asymptote is: $\mathbf{f(x) = 40}$
• The horizontal asymptote means that, the number of deer will never be less than 40

The equation is given as:

$\mathbf{f(x) = \frac{40 + 2x}{1 + 0.05x}}$

 

Expand the numerator

$\mathbf{f(x) = \frac{40(1 + 0.05x)}{1 + 0.05x}}$

Cancel out the common factors

$\mathbf{f(x) = 40}$

Hence, the equation of horizontal asymptote is:

$\mathbf{f(x) = 40}$

The horizontal asymptote means that, the number of deer will never be less than 40

Read more about horizontal asymptotes at:

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