Question

If you start a biology experiment with 5000000 cells and 25% of the cells are dying every minute, how long will it be before there are fewer than 1000 cells?

Answer 1

Answer:

t=29.61

Step-by-step explanation:

A (t) =Aoe^(kt)

We first need to solve for rate constant when t=1minute (i.e., A(1)), we are told that 25% dies leaving 75% to remain (0.75*(5*10^6 =3.75*10^6) =A(1))

A(1)=3.75*10^6=5*10^6*e^(1k)

e^k=(3.75*10^6)/(5*10^6)

    take the natural log on both side

ln(e^k)=ln((3.75*10^6)/(5*10^6))

k=ln(0.75)

k=-0.2877   (note the resulting negative rate constant which makes sense)

  the value of k is approximately -0.2877

now to solve for the time to decay to less than 1,000 cells

  1,000=5*10^6*e^(-0.2877t)

e^(-0.2877t)=1,000/(5*10^6)

 take natural log in both side

ln(e^(-0.2877t))=ln(1,000/(5*10^6))

-0.2877t=ln(0.0002)

-0.2877t=-8.5172

t=-8.5172/-0.2877  

t=29.604449

t is approximately 29.61