(b) On January 1, 2010 there were 10,000 squirrels living in Madison. Let t deno

Question

(b) On January 1, 2010 there were 10,000 squirrels living in Madison. Let t denote time in years since January 1, 2010 and S(t) denote the number of squirrels in Madison at time t. This squirrel population has a continuous birth rate of 8% and a natural continuous death rate of 2%. In addition, each year 250 squirrels are eaten by foxes and 150 squirrels are run over by cars. Write down a differential equation for S(t) (You do not need to define variables or give the initial condition. DO NOT SOLVE THE DIFFERENTIAL EQUATION.)

Explanation / Answer

Population at a moment is : S

Birth rate is 8%, as in increase of 0.08S

Death rate is 2%, as in decrease of 0.02S

250 + 150 die, as in 400

So, we have
dS/dt = (Growth rate) - (decay rate)

dS/dt = 0.08S - (0.02S + 400)

dS/dt = 0.06S - 400

and we have S(0) = 10000 ----> ANS

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.