Math / Algebra

Question< Unit Overview Step-by-Step Sample Problem Hints
Norman discovers a new animal species that has a lifespan of one week and has 2 offspring just before dying. At the end of the 1 st week, Norman counts 3 such animals. A week later animals, and a week after that there are 12 animals. After the 4 th week, there are 24 animals, and a week later there are 48 animals.
1. Recognize and Describe
The first term is 3 . Each term is equal to the previous term $\square$ $\square$ .
2. Classify
3. Write Recursive Formula
How many animals would there be after another week? $\square$

Studdy Solution

STEP 1

1. Each animal has a lifespan of one week and produces 2 offspring just before dying.
2. The sequence of the number of animals is given for the first few weeks.
3. We need to find the pattern in the sequence and predict the number of animals after another week.

STEP 2

1. Recognize and Describe the pattern.
2. Classify the type of sequence.
3. Write the Recursive Formula.
4. Calculate the number of animals after another week.

STEP 3

Recognize and Describe the pattern: - At the end of the 1st week, there are 3 animals. - At the end of the 2nd week, there are 6 animals. - At the end of the 3rd week, there are 12 animals. - At the end of the 4th week, there are 24 animals. - At the end of the 5th week, there are 48 animals.
Notice that each term is double the previous term. This suggests a pattern of multiplication by 2.

STEP 4

Classify the sequence: - The sequence is geometric because each term is obtained by multiplying the previous term by a constant factor, which is 2 in this case.

STEP 5

Write the Recursive Formula: - Let $a_n$ be the number of animals at the end of the $n$ -th week. - The recursive formula is $a_n = 2 \times a_{n-1}$ , with the initial condition $a_1 = 3$ .

STEP 6

Calculate the number of animals after another week (6th week): - Using the recursive formula: $a_6 = 2 \times a_5 = 2 \times 48 = 96$ .
The number of animals after another week (6th week) would be:
$\boxed{96}$

Was this helpful?

Studdy Solution

STEP 1

1. Each animal has a lifespan of one week and produces 2 offspring just before dying.
2. The sequence of the number of animals is given for the first few weeks.
3. We need to find the pattern in the sequence and predict the number of animals after another week.

STEP 2

1. Recognize and Describe the pattern.
2. Classify the type of sequence.
3. Write the Recursive Formula.
4. Calculate the number of animals after another week.

STEP 3

STEP 4

Classify the sequence: - The sequence is geometric because each term is obtained by multiplying the previous term by a constant factor, which is 2 in this case.

STEP 5

Write the Recursive Formula: - Let $a_n$ be the number of animals at the end of the $n$ -th week. - The recursive formula is $a_n = 2 \times a_{n-1}$ , with the initial condition $a_1 = 3$ .

STEP 6

Calculate the number of animals after another week (6th week): - Using the recursive formula: $a_6 = 2 \times a_5 = 2 \times 48 = 96$ .
The number of animals after another week (6th week) would be:
$\boxed{96}$

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

1. Each animal has a lifespan of one week and produces 2 offspring just before dying.2. The sequence of the number of animals is given for the first few weeks.3. We need to find the pattern in the sequence and predict the number of animals after another week.

STEP 2

1. Recognize and Describe the pattern.2. Classify the type of sequence.3. Write the Recursive Formula.4. Calculate the number of animals after another week.

STEP 3

STEP 4

Classify the sequence: - The sequence is geometric because each term is obtained by multiplying the previous term by a constant factor, which is 2 in this case.

STEP 5

Write the Recursive Formula: - Let an a_n an​ be the number of animals at the end of the n n n-th week. - The recursive formula is an=2×an−1 a_n = 2 \times a_{n-1} an​=2×an−1​, with the initial condition a1=3 a_1 = 3 a1​=3.

STEP 6

Calculate the number of animals after another week (6th week): - Using the recursive formula: a6=2×a5=2×48=96 a_6 = 2 \times a_5 = 2 \times 48 = 96 a6​=2×a5​=2×48=96. The number of animals after another week (6th week) would be:96 \boxed{96} 96​

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Each animal has a lifespan of one week and produces 2 offspring just before dying.
2. The sequence of the number of animals is given for the first few weeks.
3. We need to find the pattern in the sequence and predict the number of animals after another week.

1. Recognize and Describe the pattern.
2. Classify the type of sequence.
3. Write the Recursive Formula.
4. Calculate the number of animals after another week.

Write the Recursive Formula: - Let $a_n$ be the number of animals at the end of the $n$ -th week. - The recursive formula is $a_n = 2 \times a_{n-1}$ , with the initial condition $a_1 = 3$ .

Calculate the number of animals after another week (6th week): - Using the recursive formula: $a_6 = 2 \times a_5 = 2 \times 48 = 96$ .
The number of animals after another week (6th week) would be:
$\boxed{96}$