Final answer:
To calculate the mass of the tumor after a certain number of cell divisions, we need to know the increase in the number of cells with each division. Using the formula 2^n, where n is the number of divisions, we can find the mass of the tumor by multiplying the number of cells by the volume of each cell and the density of the cells.
Step-by-step explanation:
To calculate the mass of the tumor after a certain number of cell divisions, we need to know the increase in the number of cells with each division. Since the tumor begins with one cancer cell, and each division produces two daughter cells, the number of cells after each division can be determined using the formula 2^n, where n is the number of divisions. We can then calculate the mass of the tumor by multiplying the number of cells by the volume of each cell and the density of the cells.
a. After 10 cell divisions: The number of cells = 2^10 = 1024 cells. The volume of each cell can be approximated as a sphere with a diameter of 5µm, which gives a radius of 2.5µm. Using the formula for the volume of a sphere (V = (4/3)πr^3), the volume of each cell is approximately 65.45µm^3. Multiplying this by the density of 1g/ml, we get the mass of each cell as 65.45µg. Multiplying the mass of each cell by the number of cells, the mass of the tumor after 10 cell divisions is approximately 67.16µg.
b. After 20 cell divisions: The number of cells = 2^20 = 1,048,576 cells. Using the same calculations as before, the mass of the tumor after 20 cell divisions is approximately 68,719.48µg.
c. After 40 cell divisions: The number of cells = 2^40 = 1,099,511,627,776 cells. Using the same calculations, the mass of the tumor after 40 cell divisions is approximately 71,774,055,313.69µg.