The phosphate compounds found in many detergents are highly water soluble and are excellent fertilizers for algae. Assume that there are 5000 algae present at time t = 0, where t is the time in days, and conditions will support at most 500,000 algae. Assume that the rate of growth of algae, in the presence of sufficient phosphates, is proportional both to the number present (in thousands) and to the difference between 500,000 and the number present (in thousands).
(a) Write a differential equation using the given information. Use 0.01 for the constant of proportionality.
(b) Approximate the number present when t = 2 days, using h = 0.5 days.