We appreciate your visit to Amara monitored a cockroach infestation in an abandoned warehouse over time The table shows the cockroach population every week tex begin tabular c c hline. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To determine the type of sequence that best represents the cockroach population over time, let's analyze the data:
The cockroach population at each week is as follows:
- Week 1: 5 cockroaches
- Week 2: 30 cockroaches
- Week 3: 180 cockroaches
- Week 4: 1,080 cockroaches
- Week 5: 6,480 cockroaches
Step 1: Identify the Pattern
We'll begin by looking at the ratios of consecutive terms, as this will help us identify the type of sequence.
Calculate the ratio between the number of cockroaches in consecutive weeks:
[tex]\[
\frac{30}{5} = 6
\][/tex]
[tex]\[
\frac{180}{30} = 6
\][/tex]
[tex]\[
\frac{1,080}{180} = 6
\][/tex]
[tex]\[
\frac{6,480}{1,080} = 6
\][/tex]
Step 2: Analyze the Ratios
Since each ratio is the same (6), we observe a consistent pattern where each term is multiplied by 6 to obtain the next term.
Conclusion: Identify the Sequence Type
When the ratios between consecutive terms are constant, the sequence is known as a geometric sequence. Therefore, this situation is best represented by a geometric sequence because the number of cockroaches increases by a consistent factor of 6 each week.
The cockroach population at each week is as follows:
- Week 1: 5 cockroaches
- Week 2: 30 cockroaches
- Week 3: 180 cockroaches
- Week 4: 1,080 cockroaches
- Week 5: 6,480 cockroaches
Step 1: Identify the Pattern
We'll begin by looking at the ratios of consecutive terms, as this will help us identify the type of sequence.
Calculate the ratio between the number of cockroaches in consecutive weeks:
[tex]\[
\frac{30}{5} = 6
\][/tex]
[tex]\[
\frac{180}{30} = 6
\][/tex]
[tex]\[
\frac{1,080}{180} = 6
\][/tex]
[tex]\[
\frac{6,480}{1,080} = 6
\][/tex]
Step 2: Analyze the Ratios
Since each ratio is the same (6), we observe a consistent pattern where each term is multiplied by 6 to obtain the next term.
Conclusion: Identify the Sequence Type
When the ratios between consecutive terms are constant, the sequence is known as a geometric sequence. Therefore, this situation is best represented by a geometric sequence because the number of cockroaches increases by a consistent factor of 6 each week.
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