More points!! Please solve 22 and 23
1 answer:
For the table, we can count the circles that appear in each step of the fractal. The center is a single circle and is step 0. Step 1 sees 4 circles grow off of that one circle. Step 2 sees 4 circles grow off of each of these circles. Therefore the table should be:
Step 0 : 1 circle
Step 1 : 4 circles
Step 2 : 16 circles
Step 3: 64 circles
Using this table, we can solve the second part. This function is exponential growth and each step is a multiple of 4. Therefore, the function is
.
Step 0 : 1 circle
Step 1 : 4 circles
Step 2 : 16 circles
Step 3: 64 circles
Using this table, we can solve the second part. This function is exponential growth and each step is a multiple of 4. Therefore, the function is
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The recursive definition used to generate the sequence {3, 6, 3, 6, 3,...} is:
where
and
<em><u>Solution:</u></em>
Given sequence is 3, 6, 3, 6, 3,...
To find: recursive definition for the sequence
First term in the sequence is 3
Then you add on 3 to get to 6 as the second term
Then add -3 to get 3 as third term
This pattern goes on forever
3 + 3 = 6
6 - 3 = 3
3 + 3 = 6
6 - 3 = 3
and so on
<em><u>So we can generate a recursive definition as:</u></em>
Let be the nth term and "n" denotes the term's location
is the first term of sequence
, where
and
Here, is used to denote , we add on either +3 or -3 to the previous term to get next term