How do you solve the following problem? Suppose each cancerous cell has a radius of 5*10^-3 cm and that the doubling time for a population of cancerous cell is 20 hours. The tumor has an initial volume of 0.1cm^3. Find a formula for V(t).

Question

How do you solve the following problem? Suppose each cancerous cell has a radius of 5*10^-3 cm and that the doubling time for a population of cancerous cell is 20 hours.  The tumor has an initial volume of 0.1cm^3.  Find a formula for V(t).

anonymous · Answer

We have a Volume V.

so V(t) =KVo 

DV/dt = k

DV = kdt
..... more math to get to this below
so V(t) = Voe^kt

we know that the initial volume is 0.1cm^3. The radius of a cancerous cell is 5*10^-3 so then then the volume of one cell is 4/3pi(r)^3 = 5.23598*10^-7cm^3. So the population is initially1.91*10^5 cells by dividing the initial volume.

So from this you know the population doubles in 20 hours. Calculate the population in 20 hours and convert back to volume.Using this knowledge calculate a volume for the population in 20 hours. Then plug in all the know variables and solve for the constant k. 

t = 20

Vo= initial volume

V(t)= the one you calculate from P(t)

k= your solving for this to get a formula for the volume of the cancer at time t.

anonymous · Answer

Thanks mebs!  I didn't know if anyone was going to tackle this problem.

anonymous · Answer

I have the first part of the answer.  How do I get the formula for V(t) given 1.91*10^5?

anonymous · Answer

so you found the volume for the  double population. than just do this

V(double population) = V(initial)e^k(20hours)

solve k.