The population growth of a particular animal can be modelled using the following recurrence relation:

+1=(1)xn+1=rxn(1xn)

The population is measured as a proportion of the maximum sustainable population, given the resources available. xrepresents the proportion, and n represents the year.

For example, in year 0 if the maximum possible population was 1,000 and the current population was 500, then 0x0 would be 0.5.

r represents the rate at which the population grows.

There are two restrictions:

0x0 must be between 0 and 1 (exclusive).

r must be greater than 1.

An example of the population growing over time could look like this, where the population at 0x0 is 0.7 of its maximum potential size, and r = 1.8. All numbers are rounded to 5 decimal places.

Year	Formula	Resultant population (+1xn+1)
0x0	n/a	0.7
1x1	1.8 0.7 (10.7)	0.378
2x2	1.8 0.378 (1-0.378)	0.42321
3x3	1.8 0.42321 (1-0.42321)	0.43939
4x4	1.8 0.43939 (1-0.43939)	0.44339
5x5	1.8 0.44339 (1-0.44339)	0.44423
6x6	1.8 0.44423 (1-0.44423)	0.4444
7x7	1.8 0.4444 (1-0.4444)	0.44444
8x8	1.8 0.44444 (1-0.44444)	0.44444

You can see from the table above that when rounded to 5 decimal places, x will reach a limiting value where =+1xn=xn+1and will remain stable. This will remain true as long as 0x0 is between 0 and 1 (exclusive), and r is between 1.0 and 3.1 (exclusive).

Question

Write a recursive function, population, that returns the base value of x, accurate to 5 decimal places, when given appropriate values for r and x_in. The test code below will test your code with x_in=0.7 and r=1.8.