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JamenS
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??
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:\[\Large y(36)=2e^{(\frac{ln(2)}{3}*36)}=?\]