Problem Description:
The image shows a table with data related to the growth of a company's revenue over time. The task is to determine
when the company will reach $50,000 in revenue and
when it will reach $120,000 in revenue, based on the provided data.
Given Data:
The table shows the following information:
| Month | Revenue |
|-------|---------|
| 0 | $0 |
| 1 | $7,000 |
| 2 | $14,000 |
| 3 | $21,000 |
| 4 | $28,000 |
| 5 | $35,000 |
| 6 | $42,000 |
| 7 | $49,000 |
| 8 | $56,000 |
| 9 | $63,000 |
| 10 | $70,000 |
Observations:
1. The revenue increases linearly over time.
2. The revenue at month 0 is $0.
3. The revenue at month 1 is $7,000.
4. The revenue at month 2 is $14,000.
5. The pattern suggests that the revenue increases by $7,000 each month.
Step-by-Step Solution:
####
Step 1: Identify the Linear Relationship
From the data, we can see that the revenue increases by $7,000 each month. This indicates a linear relationship between the month and the revenue. The general form of a linear equation is:
\[
R = m \cdot t + b
\]
Where:
- \( R \) is the revenue.
- \( t \) is the time (in months).
- \( m \) is the slope (rate of change).
- \( b \) is the y-intercept (initial value).
From the data:
- The initial revenue (\( b \)) is $0 (at month 0).
- The rate of change (\( m \)) is $7,000 per month.
Thus, the equation for revenue as a function of time is:
\[
R(t) = 7000 \cdot t
\]
####
Step 2: Solve for When Revenue Reaches $50,000
We need to find the month \( t \) when the revenue \( R(t) \) is $50,000. Using the equation:
\[
50000 = 7000 \cdot t
\]
Solve for \( t \):
\[
t = \frac{50000}{7000} = \frac{50}{7} \approx 7.14
\]
Since \( t \) represents the month, and months are whole numbers, we round up to the next whole number because the revenue will not reach $50,000 until the end of the 8th month.
Thus, the company will reach $50,000 in revenue in
month 8.
####
Step 3: Solve for When Revenue Reaches $120,000
We need to find the month \( t \) when the revenue \( R(t) \) is $120,000. Using the equation:
\[
120000 = 7000 \cdot t
\]
Solve for \( t \):
\[
t = \frac{120000}{7000} = \frac{120}{7} \approx 17.14
\]
Again, since \( t \) represents the month, we round up to the next whole number because the revenue will not reach $120,000 until the end of the 18th month.
Thus, the company will reach $120,000 in revenue in
month 18.
Final Answers:
\[
\boxed{8 \text{ and } 18}
\]
Parent Tip: Review the logic above to help your child master the concept of 100 steps worksheet.
