An invasive insect population obeys

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

Problem

\dfrac{dy}{dt}=0.5 y\left(1-\dfrac{y}{800}\right)

, where

t

is measured in months. If

y(0)=1000

, approximately how many months later will the population decline to

900

insects? (a)

1.6\text{ months}

(b)

1.2\text{ months}

(c)

0.6\text{ months}

(d)

2.3\text{ months}