# [SOLVED] Diffucult intro to calculus problem

• Nov 23rd 2008, 02:45 PM
Sm10389
[SOLVED] Diffucult intro to calculus problem
Coming from Calculus 1, section on introduction to differential equations.

Corruption in Government-
The number of people implicated in a certain major government scandal increases at a rate jointly proportional to the number of people already implicated and the number involved who have yet been implicated. Suppose 7 people were implicated when a Washington newspaper first made the scandal public, that 9 more were implicated over the next 3 months, and that another 12 people were implicated during the following 3 months. Approximately how many people are involved in the scandal?
[Warning: This problem will test your algebraic ingenuity!]

Anyone have any clues on how to begin this bad boy?
• Nov 23rd 2008, 03:15 PM
skeeter
Quote:

Anyone have any clues on how to begin this bad boy?
do a google search on the calculus model for logistic growth ... and yes, it's a bad boy for a beginner.
• Nov 23rd 2008, 03:23 PM
CaptainBlack
Quote:

Originally Posted by Sm10389
Coming from Calculus 1, section on introduction to differential equations.

Corruption in Government-
The number of people implicated in a certain major government scandal increases at a rate jointly proportional to the number of people already implicated and the number involved who have yet been implicated. Suppose 7 people were implicated when a Washington newspaper first made the scandal public, that 9 more were implicated over the next 3 months, and that another 12 people were implicated during the following 3 months. Approximately how many people are involved in the scandal?
[Warning: This problem will test your algebraic ingenuity!]

Anyone have any clues on how to begin this bad boy?

The number implicated n satisfies the differential equation:

dn/dt=k n(N-n)

where k is a constant of proportianality, and N is the tital number involved.

9 additional people implicated in the first 3 months gives a rate of increase of ~3 per month after 1.5 months and the number involved at that time is ~=7+4.5=11.5.

This gives you your first equation:

3=k 11.5(N-11.5)

Over the nest three months 12 new people were implicated so the rate of implication is now ~4 per month, at 4.5 months when the number implicated is ~=16+6=22.

This gives us out second equation:

4=k 22(N-22).

Now solve the pair of equations for k and N

CB
• Nov 23rd 2008, 04:18 PM
Sm10389
why is there an n outside the parenthesis?
why do you use 1.5 months and 4.5 months?
how would i solve k and n with two variables in one equation?

• Nov 23rd 2008, 08:34 PM
CaptainBlack
Quote:

Originally Posted by Sm10389
why is there an n outside the parenthesis?
why do you use 1.5 months and 4.5 months?
how would i solve k and n with two variables in one equation?