Question

A rabbit matures at 6 months, and has a gestation period of 30 days (call it one month) with a 4 week time lapse after birth to become fertile again (call it one month). We will assume that we start with one breeding pair of rabbits and that each litter contains 10 rabbits, half of which are female. Such a population of rabbits increases as shown in the table below. Month: 0 1 2 3 4 5 6 7 8 9 10 11 12 Population: 2 12 12 22 22 32 32 92 92 202 202 362 362 14. How would you make a decision about which type of function to use to model a population such as this population of rabbits?

Answer 1

exponential regression

y = a b^x

ln y = ln a + x ln b

running regression of ln y on x

Month	Population	ln y
0	2	0.693147
1	12	2.484907
2	12	2.484907
3	22	3.091042
4	22	3.091042
5	32	3.465736
6	32	3.465736
7	92	4.521789
8	92	4.521789
9	202	5.308268
10	202	5.308268
11	362	5.891644
12	362	5.891644

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.970939707
R Square	0.942723915
Adjusted R Square	0.937516998
Standard Error	0.386101875
Observations	13
ANOVA
	df	SS	MS	F	Significance F
Regression	1	26.99029948	26.99029948	181.0522313	3.55662E-08
Residual	11	1.639821239	0.149074658
Total	12	28.63012072
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	1.55249915	0.202372371	7.671497571	9.70982E-06	1.107080565
Month	0.385095246	0.028619775	13.45556507	3.55662E-08	0.322103546

ln y = 1.5525 + 0.3851 x

y = e^(1.5525 + 0.3851 x)

= 4.723263 * 1.46975 ^x