To devise an equation that represents the number of injections needed per month, we need to consider the pattern provided.
Let's break it down step by step:
1. In the first month, there is one injection.
2. In the second, third, fourth, and fifth months, there is one injection per month.
3. In the sixth, seventh, and eighth months, there are three injections in total, with two months between each pair of injections.
4. After the eighth month, the cycle repeats, with the same pattern of three injections every two months.
Based on this pattern, we can summarize the number of injections per month as follows:
- For the first five months: 1 injection per month
- For the sixth, seventh, and eighth months: 3 injections in total, with two months between each pair
- After the eighth month: the cycle repeats again
Now let's devise an equation to represent this pattern:
Let n represent the number of months passed. We need to account for three scenarios:
1. For the first five months (n ≤ 5): There is one injection per month.
2. For the sixth, seventh, and eighth months (6 ≤ n ≤ 8): There are three injections over two months. We can calculate this as 1 + n - 5 (one injection per month, plus the additional injections).
3. After the eighth month (n > 8): The cycle repeats. We can compute this as 3 * ((n - 9) // 2) + 3 (three injections every two months, starting from the ninth month).
Combining these scenarios, the equation that represents the number of injections needed per month (Y-axis) based on time (X-axis) is:
Y =
1 ; if n ≤ 5
1 + n - 5 ; if 6 ≤ n ≤ 8
3 * ((n - 9) // 2) + 3 ; if n > 8
Note: The double forward slash (//) signifies integer division, which discards the decimal part of the result.
With this equation, you can determine the number of injections required per month by plugging in the value of n, representing the number of months passed, on the X-axis.