# What is the ratio after 1 month given certain conditions?

• caters
In summary: I will provide a summary of the conversation for clarification.In summary, the problem involves calculating the rate of population growth starting from a population of 100,000. The first 3 steps have already been completed, including calculating the sex ratio, cycle ratio, and pregnancy ratio. The next step is to determine the pregnancy ratio after one month of trying for pregnancy. The cycle length is verified to be 4, and the ratio of pregnant to non-pregnant individuals in the fertile window is found to be 2:3. The effectiveness of anti-miscarriage medication is also taken into account. The final calculation shows that approximately 31.2% of the population becomes pregnant after one month of trying, with a miscarriage rate of
caters
Homework Statement
Given certain conditions, what percentage of the population is pregnant after 1 month of trying. Assume that no reproductive assistance therapy is done.
Relevant Equations
$$People_{Pregnant_n} = People_{Concieved} + People_{Pregnant_{n-1}} - Miscarriages_{Total}$$
$$People_{Concieved} = People_{Fertile} * \frac{2}{3}$$
$$Miscarriages_{Total} = (People_{Pregnant_3} * 30.9\%) + (People_{Pregnant_4} * (35.4\% * 60\%)) + (People_{Pregnant_5} * (26.9\% * 70\%))$$
So this question is a math question having to do with me calculating the rate of population growth starting from a population of 100,000. I have already gotten the first 3 steps done (sex ratio, ratio of cycle time, and pregnancy ratio) after a week among those in the fertile timeframe (calculating the ratio amongst the entire female population, which is what I'm after, should be relatively easy afterwards).

Monthly Cycle numbers

Here is the cycle ratio:

$$2_{early}:2_{fertile}:1_{late}$$

And the numbers:

$$20,000_{early}:20,000_{fertile}:10,000_{late}$$

Now, let's divide the early into 2 groups, pre-fertile, and safe and assume there is a 50/50 split between those 2 groups. Let's also assume that all the people in the fertile group are in the late group after a week, all those that are in the late group, are in the safe group after a week and so on. This suggests a cycle length of $4$, but let me verify it.

After a week:

$$10,000_{safe}:10,000_{pre-fertile}:10,000_{fertile}:20,000_{late}$$

After 2 weeks:

$$20,000_{safe}:10,000_{pre-fertile}:10,000_{fertile}: 10,000_{late}$$

After 3 weeks:

$$10,000_{safe}:20,000_{pre-fertile}:10,000_{fertile}:10,000_{late}$$

Yep, cycle length of $4$ is confirmed. To get the pregnancy ratio after a month of trying for pregnancy, I need the exact division which is a tad more complicated.

Figuring out pregnancy ratio

The ratio amongst the people in the fertile window of people who become pregnant is $2:3$ or $40\%$ Anti-miscarriage meds only work at or after 4 weeks has passed(more specifically, 4 weeks from the safe part of the cycle). Their effectiveness is $60\%$ at 4 weeks and $70\%$ at 5 weeks. It is 100% effective at 6 weeks. Here are the miscarriage rates:

- 3 weeks: 30.9%
- 4 weeks: 35.4%
- 5 weeks: 26.9%

So for the first week, $8,000$ become pregnant and the other $12,000$ in the fertile window go on to be in the late group. Ratio is $8,000_{pregnant}:42,000_{non-pregnant}$ which simplifies to $4:21$ or in terms of percents, $16\%$ of the female population.

After a week, another $4,000$ become pregnant. However, 30.9% of those from the starting week have a miscarriage. That is $2472$ people who miscarried, fewer than the number that became pregnant. Now the number is at $9,528$ pregnancies.

After another week, another $4,000$ become pregnant. 30.9% of those from the previous week miscarry. On top of that, 40% of the predicted 35.4% miscarry. So that is $1,236 + 783 = 2019$ miscarriages. This is fewer than those that become pregnant so there is an overall increase again. Now $11,509$ people are pregnant

After a third week, another $4,000$ become pregnant. 30.9% of those from the previous week, 40% of 35.4% of those that became pregnant the week before last, and 30% of 26.9% of those that became pregnant on the starting week miscarry. This adds up to $1,236 + 566 + 346 = 2,148$ miscarriages. Now $13,361$ people are pregnant.

After a fourth week, another $8,800$ become pregnant. At this point, there is no more push to become pregnant so the miscarriage calculations will get simpler from here. Here are the numbers for the miscarriages: $177 + 391 + 1236 = 1804$ miscarriages. Now, this is way less than the number that became pregnant so the total number of pregnancies now is $20,357$

Fifth week:

$2,719 + 391 + 192 = 3,302$ miscarriages

$17,055$ pregnancies

Sixth week:

$192 + 861 = 1,053$ miscarriages

$16,002$ pregnancies

Seventh week:

$421$ miscarriages

The final number of pregnancies is $15,581$ pregnancies

Percentage pregnant is $31.2\%$ which is approximately a $3:10$ ratio

Did I do my calculations correctly or did I make a mistake somewhere in the sea of multiplication, addition, and subtraction to calculate the miscarriage and pregnancy numbers week by week?

NOTE: My calculations assume no fertility after the miscarriage for several months, no other causes of fetal death besides spontaneous abortion(otherwise known as a miscarriage), and no maternal death while pregnant so despite matching the percent of the population that become pregnant after 1 try very closely, it might not be a realistic percentage for after 2-4 tries. Also, it is only this step, calculating the number of pregnancies that I need you to verify. Calculating how many are twins, etc. I should be able to do fine on my own.

caters said:
Homework Statement: Given certain conditions . . .
Could you please give the original problem statement? You start by saying "Given certain conditions . . .", but it is not clear what the conditions are. It seems that you have been given more information than is listed in the Homework Equations section. It is difficult to know whether you are solving the problem correctly without knowing what the problem is.

I have everything there in the post that is relevant to this specific problem having to do with the ratio of pregnant:non-pregnant after 1 month of trying(the cycle ratio(with its almost equal split), the miscarriage rates for 3, 4, and 5 weeks past the safe part of the cycle, the miscarriage equation, the conception equation, and the pregnancy equation. Also, that 2:3 ratio is supposed to be 2/5 in fraction form, don't know why I put it in as 2/3)

And I have the solution attempt organized in such a way that you see things in this order:

1. Verifying that the cycle length is 4
2. Ratio of pregnant:non-pregnant amongst those in the fertile timeframe
3. Miscarriage rates and effectiveness of anti-miscarriage meds
4. Pregnancy ratio calculation

You may have the necessary information scattered throughout your work, but that is much harder for helpers to spot and check. Please put all the given problem information at the beginning.

SammyS, tnich and WWGD

## 1. What is the ratio after 1 month if the initial amount is 100 and the growth rate is 10%?

The ratio after 1 month would be 110:100, or 1.1:1. This means that the initial amount of 100 has grown by 10% to become 110.

## 2. How does the ratio change after 1 month if the initial amount is doubled and the growth rate is 5%?

The ratio after 1 month would still be 110:100, or 1.1:1. The initial amount being doubled does not affect the growth rate, so the ratio remains the same.

## 3. What if the growth rate is negative? How does that affect the ratio after 1 month?

If the growth rate is negative, the ratio after 1 month would be smaller than the initial ratio. For example, if the initial ratio is 10:1 and the growth rate is -50%, the ratio after 1 month would be 5:1.

## 4. Can the ratio after 1 month ever be greater than the initial ratio?

Yes, if the growth rate is high enough, the ratio after 1 month can be greater than the initial ratio. For example, if the initial ratio is 10:1 and the growth rate is 100%, the ratio after 1 month would be 20:1.

## 5. How does the length of time affect the ratio? Will the ratio continue to grow or eventually reach a limit?

The length of time does affect the ratio, as a longer time period allows for more growth. However, the growth rate also plays a significant role. If the growth rate is high, the ratio will continue to grow. But if the growth rate is low or negative, the ratio may eventually reach a limit.

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