Please help.

Assume that a cell culture has a density of 10^8 cells/mL. You transfer 20 microliters of this culture onto the microscope slide.
A) How many cells do you expect will be in this 20 microliters drop you placed under the microscope?

B) You add to your sample above an equal volume of a liquid dye, India Ink solution. You transfer 20 microliters of this mixture onto a microscope slide. How many cells do you expect will be now on this 20 microliters drop you placed under the microscope?

2000000 cells

a) 2,000,000 cells

b) 1,000,000 cells

To calculate the number of cells in a given volume, we can use the formula:

Number of cells = cell density (cells/mL) × volume (mL)

Given:
Cell culture density = 10^8 cells/mL
Volume transferred = 20 microliters (µL)

A) To calculate the number of cells in the 20 microliters drop:
1 mL = 1000 µL

Number of cells = 10^8 cells/mL × (20 µL / 1000 µL/mL)
= 10^8 cells/mL × (0.02 mL)
= 2 × 10^6 cells

Therefore, you would expect about 2 million cells in the 20 microliters of the culture drop placed under the microscope.

B) If you add an equal volume of India Ink solution (20 µL) to the cell culture drop, the total volume of the mixture becomes 40 µL.

To calculate the number of cells in this new drop:

Number of cells = 10^8 cells/mL × (40 µL / 1000 µL/mL)
= 10^8 cells/mL × (0.04 mL)
= 4 × 10^6 cells

Therefore, you would expect about 4 million cells in the 20 microliters drop after adding the India Ink solution.

To answer these questions, we will need to use the given information and apply some calculations.

A) To determine the number of cells in the 20 microliters drop, we need to know the volume of the original cell culture. Since the culture has a density of 10^8 cells/mL, we can assume that the entire culture has this density.

To find the initial volume, we need to know the total number of cells. Assuming the density is uniform throughout the culture, we can calculate this by multiplying the density by the total volume.

Number of cells = density * volume

Here, the volume is unknown but can be determined using the given information:

10^8 cells/mL * volume = number of cells

Now, we can solve for the volume:

volume = number of cells / 10^8 cells/mL

Since the 20 microliters of culture was transferred to the microscope slide, we can determine the number of cells in this drop by multiplying the volume by the density:

Number of cells in the 20 microliters drop = 20 microliters * density

B) After adding the India Ink solution with an equal volume to the cell culture, the total volume will be doubled. Therefore, the final volume of the mixture will be 20 microliters + 20 microliters = 40 microliters.

To calculate the number of cells in this 40 microliters drop, we can use the same formula as before:

Number of cells in the 40 microliters drop = 40 microliters * density

Now, let's substitute the given density value into the formulas to find the answers:

A) Number of cells in the 20 microliters drop:
Number of cells = (number of cells / 10^8 cells/mL) * 20 microliters

B) Number of cells in the 40 microliters drop:
Number of cells = (number of cells / 10^8 cells/mL) * 40 microliters

By substituting the appropriate values, you can calculate the actual number of cells in each case.