b This time, we do not know the number of rabbits for two months. How would you go about finding the common ratio now?
A
aTable:
B
bTable:
Practice makes perfect
a Since the growth of the rabbits multiplies, the number of rabbits can be described by a geometric sequence.
GEOMETRIC SEQUENCE
t(n)= t(0) r^n
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&Zeroth Term: t(0)
&Common Ratio: r
To determine the common ratio, we have to divide the number of rabbits during any given month with the previous month's number of rabbits. Since 124=3, this is the common ratio. With this information we can fill out the rest of the table of values.
b Just like in Part A, we have a geometric progression of the number of rabbits. However, this time we do not have the number of rabbits for two months in a row.
To find r we have to multiply the number of rabbits from the beginning by r twice and equate the product with the number of rabbits in month 2, which is 24.
Notice that the common ratio in a geometric progression is always positive, which is why we disregard the negative solution. The common ratio is 2. Now we can complete the table.
