1. Section 5.1 - 5. Sequences - Core Connections Integrated I, 2013

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} 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

\frac{1 2}{4} = 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 .

6 r^{2} = 24

DivEqn

$LHS / 6 = RHS / 6$

r^{2} = 4

SqrtEqn

$LHS = RHS$

r = \pm 2

$r > 0$

r = 2

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.

Exercise 6 Page 250