Question

HELP...
Daisy purchased a rabbit couple to keep as pets. Perhaps Daisy got more than she bargained for! If the population of rabbits doubles every 3 months, how many rabbits will Daisy have at the end of 3 years? (Hints: Remember that your starting number is 2. The exponent is determined by the number of periods of doubling. Use your calculator.)


a.2048

b.512

c.256

d.8192


D??

Answer 1

This is an exponent growth problem. To solve it, you first need to know the formula:\[y(t)=ae^{kt}\]where t is the time, a is the initial amount and k is the rate of growth.

For this problem, the formula would start out as as follows since you know that the amount doubled from 2 to 4 in 3 months:\[4=2e^{3k}\]Now solve for k:\[2=e^{3k}\]\[ln(2)=ln(e^{3k})\]\[ln(2)=3k\]\[\frac{ln(2)}{3}=k\]
Now that you know k, plug in t for 3 years (36 months) with a starting amount of 2:\[\Large y(36)=2e^{(\frac{ln(2)}{3}*36)}=?\]

Answer 2

i got 8192?

Answer 3

That's correct