Question

A savings account is opened with $15 and increases monthly by 20%. Complete the graph of the geometric sequence by labeling the points.(2 points)
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Remaining Attempts : 3

Answer 1

To complete the graph of the geometric sequence for the savings account that starts with $15 and increases by 20% monthly, we first need to find the terms of the sequence.

In a geometric sequence, each term can be found using the formula:

\[
a_n = a_1 \cdot r^{(n-1)}
\]

Where:
- \(a_n\) is the nth term,
- \(a_1\) is the first term (initial amount),
- \(r\) is the common ratio (1 + percentage increase),
- \(n\) is the term number.

In this case:
- \(a_1 = 15\),
- The percentage increase is 20%, so \(r = 1 + 0.20 = 1.20\).

Now, we’ll calculate the first few terms of the sequence:

1. **First month (n=1)**:
\[
a_1 = 15
\]

2. **Second month (n=2)**:
\[
a_2 = 15 \cdot (1.20)^{(2-1)} = 15 \cdot 1.20 = 18
\]

3. **Third month (n=3)**:
\[
a_3 = 15 \cdot (1.20)^{(3-1)} = 15 \cdot (1.20)^{2} = 15 \cdot 1.44 = 21.60
\]

4. **Fourth month (n=4)**:
\[
a_4 = 15 \cdot (1.20)^{(4-1)} = 15 \cdot (1.20)^{3} \approx 15 \cdot 1.728 = 25.92
\]

5. **Fifth month (n=5)**:
\[
a_5 = 15 \cdot (1.20)^{(5-1)} = 15 \cdot (1.20)^{4} \approx 15 \cdot 2.0736 = 31.10
\]

Now we can summarize the values calculated:

- Month 1: $15
- Month 2: $18
- Month 3: $21.60
- Month 4: $25.92
- Month 5: $31.10

You can plot these points on a graph with the x-axis representing the month (1 to 5) and the y-axis representing the amount in the savings account. Label the points accordingly:

- (1, 15)
- (2, 18)
- (3, 21.60)
- (4, 25.92)
- (5, 31.10)

This completes your geometric sequence and the required labeling for the points on the graph.