168
HL Unit 7 (Differential Equations)
Figure 7.2: Slope field for problem 4
(a) If P (0) = 3, what is lim P (t)? If P (0) = 3, what is lim P (t)? If t→∞
t→∞
P (0) = 0, what is lim P (t)? t→∞
(b) If P (0) = 3, for what value of P is the population growing the fastest? (c) Find P (t) if P (0) = 3. (d) A different population is modeled by a function Y that satisfies the separable differential equation dY Y t = 1− dt 5 12 Find Y (t) if Y (0) = 3. (e) What is lim ? t→∞
h
Ans: 12, 12, 0; 6; P (t) =
12 1+3e−t/5
t
t2
;Y (t) = 3e 5 − 120 ; 0
i
Mr. Budd, compiled September 29, 2010