Question

a combination of drugs gives 99% cell kill per cycle.

Patients tumor mass is 10^11 cells before treatment.How many

cycles of this combination are needed to reach zero cell population

(or less than one)?

Answer 1

Number of cells before treatment = 1011
Number of cells after 1 cycle = 0.01 * 1011 = 109
Number of cells after 2 cycles = 0.01 * 109 = 107

Therefore, the number of cells after n cycles = (10-2)n * 1011

For there to be less than 1 cell;

1 = (10-2)n * 1011
=> 11 - 2n = 0

Since the Left Side is 1, the right side has to be 1 as well, for which the two exponents must equal zero, since x0 = 1.

=> n = 11/2 = 5.5

Therefore, there need to be atleast 5.5 ( or 6 cycles as the number of cycles cannot be a fraction) for the number of cancerous cells in the patient to be less tahn 1.