A cancerous cell lacks normal biological growth regulation a

A cancerous cell lacks normal biological growth regulation and can divide continuously. Suppose a single mouse skin cell is cancerous mitotic cell cycle (the time for the cell to once) is 20 hours. The number of cells at time t grows according to an exponential model. (a) Find a formula C (t) for the number of cancerous skin cells after t hours. C(t) = (b) Assume atypical mouse skin cell is spherical of radius 50 times 10^-1 cm. Find the combined volume of all cancerous skin cells after t hours. (If you write out the constant multiplier in your exponential model, it will start with many 0s. Ether enter an exact number or continue up to the first non- zero digit in your answer. All other numbers in the model either need to be exact or correct to at least three digits.) Combined volume V(t) = When will the volume of cancerous cells be 1 cm?

Solution

since the cell divides continuously

time to divide is 20 hours

that is at 20 hours cells would be 2

applying eponential growth formula

A = P e^kt

2 = e^(20k)

ln 2 / 20 = k

k = 0.034657

hence, the formula is

C(t) = e^0.034657t

b) volume of sphere = 4/3 pir^3

combined volume = 4/3 pir^3 * e^0.034657t

= 4/3 pi * ( 50* 10^-4)^3 * e^0.034657t

= 5.233* 10^-7 e^0.034657t

c) plugging V(t) = 1

1 = 5.233* 10^-7 e^0.034657t

ln 1.9109 * 10^6 = e^0.034657t

t = 417 hours