I have a number of patients this month who need to start a course of treatment.
The treatment involves an injection now, followed by 4 more injections at monthly intervals, and then 3 more injections 2 months apart. That's a total of 8 injections in 1 year.
Each month, I have a new batch of patients who start treatment.
So, as time goes on, each month, more injections need to be done. We will need to do more injections in January 2017 compared to the number of injections in January 2016. We will need to do way more injections in January 2018.
Could you please devise an equation that will tell me <how many injections are needed per month> on the Y-axis vs <time> on the X-axis?
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.