Question

The population of rabbits in East Fremont is 250 in September of 2004, and growing at a rate of 3.5% each month. If the rate of population growth remains constant, determine the month and year in which the rabbit population will reach 128,000?

Answer 1

In October of `2019` rabbit population will reach `225,000`

Explanation:

Rabbit population in sept 2004 is `P_i= 250`

Rate of monthly population growth is `r=3.5%`

Final population after `n` months is `P_f=128000 ; n= ?`

We know `P_f = P_i(1+r/100)^n or P_f / P_i = (1+r/100)^n`

Taking log on both sides we get `log(P_f)-log(P_i) = n log (1+r/100) or n= (log(P_f)-log(P_i))/log (1+r/100)= (log(128000)-log(250))/log(1.035)=181.34(2dp) :.n ~~ 181.34` months `= 15` years and `1.34` month.

In October of `2019` rabbit population will reach `225,000` [Ans]