Suppose that 200 fish are introduced into a protected lake. The fish population can be approximated by P (t) = 200+40t/1+0.05t, with t being the time in years since the fish were introduced into the lake. 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 fish population and the number of years since the fish were introduced into the lake).

y=800

the poblation of fish grows to 800 in more than 20 years

Step-by-step explanation:

Remember that an asymptote is a line that the graph of a function approaches but never touches. Rational functions contain asymptotes

The method used to find the horizontal asymptote changes depending on how the degrees of the polynomials in the numerator and denominator of the function compare.

First we must compare the degrees of the polynomials. Both the numerator and denominator are 1st degree polynomials. Since they are the same degree, we must divide the coefficients of the highest terms. In the numerator, the coefficient of the highest term is 40, in the denominator is 0.05 so if we divide these so the horizontal asymptote is at y = 800.

With this result and the function we can think the fish's poblation grows to 800 and if we prove the function for t 1, 5, 10, 15, 20 we can calculate P (t) until it be equal to 800 o near because remember an asymptote never touchs the limit