Statistics:
0 - foundation year = 1 678 (62% females)
Population at end of year one = 5 333 fish (male and female)
Population at end of year two = 16 545 (male and female)
Population at end of year three = 38 432 (male and female)
Population at end of year four = 28 344 (male and female)
I = rN
I = the increase to the end of year four.
28 344 - 38 432 = -10 088
Notice that this is a negative number because of the loss in population during year four.
-10 088 is the number of fish lost during the fourth year
Therefore I = -10 088 (male and female fish)
-10 088 = rN
-10 088 = r(38 432 * 0.62)
N = the number at the START of the year. For year four that is the population at the end of year three.
Remember that ONLY females count in these calculations. So you must correct for females by multiplying the total population of male and female fish by the percent of females. This was 62%. This is changed to decimal form - 0.62.
-10 088 = r(23 827.84)
For practical purposes we don't want to deal with "fractional" fish - so round to the nearest whole fish. 23 827.84 becomes 23 828 fish.
Now you complete the calculation for year four as follows:
-10 088/23 828 = r
Now solve for the intrinsic rate (r) by dividing 23 828 into -10 098.
-0.42 = r
This is the intrinsic rate of increase for the population. Since the value is less than "1" the population has decreased.