Doctors monitoring the growth of tumor cells in a cancer patient know that the i

Question

Doctors monitoring the growth of tumor cells in a cancer patient know that the initial tumor cell count was 600 and that the cell growth is increasing at a rate of 22.5% per day.

A. Write an exponential function to model the number N of cancer cells t days after the initial reading.

B. Write the equivalent logarithmic function model. What do the independent and dependent variables in the model represent?

C. The type of treatment prescribed for the patient is determined by how fast the tumor cells are growing. The doctors use 60,000 cells as their benchmark number. How many days after the initial cell count will this occur?

Explanation / Answer

A) Initially there are 600 cells. After one day

It is 600 + 0.225(600) = 600 (1 + 0.225) = 600(1.225)

After another day, the cell-count is {600 (1.225)} x 1.225

After 3 days, the count is [{600 (1.225)} x 1.225] x 1.225

After t days, the count will be 600 x 1.225^t

B) Logarithmic model:

N = 600 (1.225^t)

log N = log 600 + t log 1.225

N which is equal to number of cancel cells after t days. N here is dependent variable and t is an independent varriable.

C) Given N = 60000

60000 = 600 (1.225^t)

1.225^t = 100

t = log 100/log1.225

t = 22.69 days

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