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Expert: - 11/30/2008


Question
Certain animal, current population 350, is growing 3% each year if left to itself, but hunters kill 15 of the animal each year.

1.   generate a difference equation which describes the population change year to year
2.   How many will there be in 15 years?
3.   Find the limit when the year tends to infinity
4.   Will the population eventually double? If so, how long this takes?
5.   Will the population die out? If so, how long this takes?  

Answer
Let x be the number of years.

1. The equation for each year is integer(350(1.03)) - 15, since these are animals we are talking about.  There can't be half a deer, at least, I haven't seen one.  I would say you have to use this to generate values for each of the years.

2. I would work out each year giving
  350
1   345
2   340
3   335
4   330
5   324
6   318
7   312
8   306
9   300
10   294
11   287
12   280
13   273
14   266
15   258

3. If this continues, the population is at risk and some year may be
anniilated.

4. From what I'm given, the population will never double.

5. At this rate, is should take 39 years.  Do it in Excel with each row as =INT(B1*1.03)-15.  A1:A40 should have a 1 through 40.  B1 should have a 350.  B2 should have what was given and can be copied down.

Again, since this is a population, I keep to integer answers for each year.

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