Question

300 450 1 +0.050 3. S points. Suppose that 300 fish are introduced into a protected lake. The fish population can be approximated by P(t) = with 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). Hint: remember that we are looking for an equation for the horizontal asymptote, and not just a number. (An equation must be in the form "y")

Answer 1

sol y=800 than 20 years in more 900 the problapopulation of fish grow Explanation! contain asymptotes method en the fonction compare that asymptate Remember line that the graph of a fonction approaches but never touches Rational functions The used to find the horizontal asymptote changes depending how the of the degrees numerator and polynomials in of the denominator the first, we compare polynomials. Both the numerator and denominator are it degree polynomials. Since they degree , we must divide the coefficients of the of the highest terms. In the numerator the coefficient of the term is "40" in the must degrees of the are same degree highest

denominator these is "0.05". so if we divide so the horizontal asymptote is at 'y=800 [: Y= 005 40 with this result and the function think the fishs if poblation can ce to we and 200 1,5,lo, + grows prove for the function Plt) cao we OY 15 120 calculate until it be "equal to 80019 becaure near an remember asymptote never touches the limit":