The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Courses » ap-calculus

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Tricky logistic growth problem
Replies: 5   Last Post: Apr 29, 1998 7:45 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Elisse Ghitelman

Posts: 34
Registered: 12/6/04
Tricky logistic growth problem
Posted: Apr 27, 1998 12:30 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In light of Dave Slomer's problem of assigning "difficult" problems, I sat
down today and worked a practice AP exam from the new Barron's review book
before having my students try it. (It's our school vacation week). I ran
into a problem on part A of the multiple choice (NO calculators) that I'm
not sure how to do without a calculator. I only have a copy of the problem
(not the book with the solutions) at home with me, so I'm looking for a
little help. Here's the problem:

A population of rabbits grows according to the differential equation
dR/dt = 0.001 R (200 - R) where R(t) is the number of rabbits after t months.
If there were initially 25 rabbits, aproximately how many months will it
take the population to double?

(a) 2.7 (B) 3.5 (C) 4.2 (D) 6.9 (E) 8.4

I tried two different techniques: First, I tried to use Euler's method by
hand with one month intervals. I had to do a lot of rounding to get
numbers I could work with, and then just guessed based on the answer
choices. I saw that the population was initially growing at around 5
rabbits/ month; since I was below half the limiting population, the growth
rate was increasing, so it would take a little less than five months, guess
choice (C).

Next, I actually solved the diff eq to get:
R/(200-R)=(1/7) e^(t/5)
Substituting R=50, you get that the doubling time is t = 5 ln(7/3).
Again, I estimated; ln (7/3) is a little less than 1, so we guess (C) again.

So, anyone with too much time on their hands, and more insight than I want
to suggest an easier way to get the answer for this one.

Thanks in advance for your help.

Elisse Ghitelman
Newton North High School
Newton, MA, USA

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.