Math 242 Group Problems Section 1.4-1.5
1. The growth rate, r, for a population is a function of the current population, P. The graph of this
function is shown below. This particular relationship gives rise to a logistic growth model that
includes harvesting.
r
(a) The values of P for which r = 0 are called equilibrium points. Estimate the equilibrium points
for this population.
(b) For what size populations is the growth rate negative?
(c) For what population size is the growth rate at an absolute maximum?
(d) For what size populations is the growth rate increasing?
2. The graph of the velocity function v = f(t) for a bungee jumper is shown. A positive velocity
indicates that the jumper is traveling upwards away from the ground, and a negative velocity
indicates the jumper is traveling downwards toward the ground. (Note: speed is given by the
absolute value of velocity.)
v (miles per hour)
(a) Estimate f(6) and f(18), and give their meaning in practical terms.
(b) Which value is greater, f(2) or f(10)?
(c) When is the jumper traveling faster, at t = 2 or at t = 10?
(d) During what time intervals is the bungee jumper traveling upward?
(e) What is happening to the jumper at the t-intercepts?
(f) Estimate the global extrema of f, and explain the practical significance of each.
(g) An object experiences a deceleration when its speed, which is the absolute value of the
velocity, is decreasing. During the first 10 seconds, when is the bungee jumper decelerating?
3. The graph of the function y = f(x) is shown. Show how to represent the following as directed
distances (lengths).
(a) f(a)
(b) f(b)
(c) b – a
(d) f(b) – f(a)
a b
t (seconds)
v = f(t)
P
r = g(P)
x
y y = f(x)