At puberty, a female has more than 400,000 immature egg cells in her ovaries. Calculate the percentage of these eggs that will ovulate, assuming that 13 ovarian cycles occurs per year in her reproductive life span of 40 years.

Options

A. `52%`
B. `0.13%`
C. `5.2`
D. `13%`

Answer

To solve the problem of calculating the percentage of immature egg cells that will ovulate in a female's reproductive lifespan, we will follow these steps:

### Step 1: Determine the total number of immature egg cells
At puberty, a female has more than 400,000 immature egg cells in her ovaries. We can denote this number as:
\[ n = 400,000 \]

### Step 2: Calculate the number of ovulation cycles in a year
It is given that a female has 13 ovarian cycles per year. Thus, the number of ovulation cycles per year is:
\[ \text{Cycles per year} = 13 \]

### Step 3: Calculate the reproductive lifespan in years
The reproductive lifespan of a female is given as 40 years. Therefore, the total number of years is:
\[ \text{Reproductive lifespan} = 40 \]

### Step 4: Calculate the total number of ovulation cycles over the reproductive lifespan
To find the total number of ovulations, we multiply the number of cycles per year by the number of years in the reproductive lifespan:
\[ \text{Total ovulations} = \text{Cycles per year} \times \text{Reproductive lifespan} \]
\[ \text{Total ovulations} = 13 \times 40 = 520 \]

### Step 5: Calculate the percentage of eggs that will ovulate
Now, we need to find the percentage of the total immature eggs that will ovulate. We do this by dividing the total number of ovulations by the total number of immature eggs and then multiplying by 100 to convert it to a percentage:
\[ \text{Percentage of eggs that will ovulate} = \left( \frac{\text{Total ovulations}}{n} \right) \times 100 \]
\[ \text{Percentage of eggs that will ovulate} = \left( \frac{520}{400,000} \right) \times 100 \]

### Step 6: Perform the calculation
Now we perform the calculation:
\[ \text{Percentage of eggs that will ovulate} = \left( \frac{520}{400,000} \right) \times 100 = 0.13\% \]

### Final Answer
The percentage of immature egg cells that will ovulate is:
\[ \text{Answer} = 0.13\% \]

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