Question

Certain bunny rabbits reproduce at a continuous rate of 200% a year. Assuming that a warren starts with 10 bunny rabbits calculate the number of rabbits after 3 years (assume none of the bunny rabbits meet with misadventure).A. 6072
B. 4034
C. 32
D. 561
E. 23
F. 123

Answer 1

Answer:

The correct option would be 'B. 4034'.

Step-by-step explanation:

If a population grows continuously

Then the final population is

$P=P_{0}e^{rt}$

Where,

$P_{0}$ = Initial population

t = Number of period

r = rate of increasing per period

We have

$P_{0}$ = 10

r = 200%= 2  $(\because 1\%=\frac{1}{100})$

t = 3 years

Hence, the population of rabbits, after 3 years is,

$P=10e^{2\times 3}$

$P=10e^6$

$P\approx 4034$

Therefore, option B is correct.