Question

With over 30 million rabbits, the bunny farm is getting overcrowded and some of the rabbits are dying from a contagious disease.  The rabbits have stopped reproducing, and the disease is reducing the total rabbit population at a rate of about 30% each month.  If this continues, then in how many months will the population drop below 100 rabbits? (For t(0), use your number from part b.)

Answer 1

30,000,000 * 0.7^t < 100
0.7^t < 1/300,000
t > -log(300,000)/log(0.7)
t > 35.36

Answer 2

100%-30%= 70%, so 70/100= 0.7
0.7 is your multiplier that mean he started at 30,000,000 rabbits which is your initial value. So the equation looks like this. t(n)= 30,000,000*(0.7)^n
t(n)= 30,000,000*(0.7)^36
t(n)= 79.5519253757896 which is estimated by 79.56
Therefore, in the month of 36 is where the population of rabbits will be below 100 rabbits.