A canoe starts from rest on a calm lake

MATHEMATICS · Single correct · AP · Calculus BC · Differential Equations · Differential Equations

Problem

A canoe starts from rest on a calm lake. For

0\le t<3

seconds its velocity

v(t)

(in m/s) satisfies

\dfrac{dv}{dt} = -0.4v + 1.2

. For

t\ge 3

seconds the paddler reduces effort so that

\dfrac{dv}{dt} = -0.4v + 0.6

. Using a constant step size of

2

seconds, which of the following is the BEST estimate of the canoe’s velocity at

t=4

seconds obtained by two tangent-line steps? (a)

4.80\text{ m/s}

(b)

2.88\text{ m/s}

(c)

3.36\text{ m/s}

(d)

1.68\text{ m/s}