Let P(t) represent the number of students in a school who buy their lunch after t weeks. Suppose P is increasing at a rate proportional to 600-P where the constant of proportionality is k. Suppose 300 students buy their lunch initially and 400 buy their lunches after 10 weeks.
a.) Write and solve a differential equation that describes this situation.
b.) How many students will buy their lunch after 20 weeks?
c.) If school were to go on endlessly, what is the limit to the number of students buying lunch
Please help as I've been stuck on this problem for a while