A population of rabbits follows the law of uninhibited growth. There are 5 rabbits initially and after 4 months there are 35. a.) How many rabbits will there be in one year? b.) How long will it take for the initial population to triple?

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Answer 1 · 2017-06-25T12:06:21

a) Rabbit population after $12$ months is $1715$ and b) will tripple , i.e $15$ after $2.2583$ months.

The formula for uninhibited growth of rabbit is $P_t=P_i*e^(kt)$ ,

where $P_t,P_i,k,t$ are population, initial population,

growth constant, and period in months.

$P_4=35 , P_i=5,t=4 , k = ? :. 35 =5*e^(k*4) or e^(4k) =7$ . Taking log on both sides, we get,

$4k=ln7 ; [lne=1] or k =ln7/4 = 0.486478$

a) $k= 0.486478 , P_12=? :. P_12 = P_i*e^(kt)$ or

$P_12 = 5*e^(0.486478 *12) = 1715$

b) $P_t=15 ; t =? :. 15 = 5 * e^(0.486478*t)$ or

$e^(0.486478*t) = 15/5=3$ Taking log on both sides, we get,

$0.486478*t= ln 3 :. t= ln3/0.486478= 2.2583$ months

a) Rabbit population after $12$ months is $1715$ and b) will tripple ,

i.e $15$ after $2.2583$ months [Ans]