Question

suppose in an experiment you started with 100000 cells and observed that the cell population decreased by one half every minute. determine how long it would take the cell population to reach 10.

Answer 1

P is the population

x is the time and minutes

the equation of this problem

$P(x)=100000\cdot(\frac{1}{2})^x$

Then we have that P(x)=10, so we need to find the value of x

$10=100000\cdot(\frac{1}{2})^x$

then we need to isolate the x

$\frac{10}{100000}=(\frac{1}{2})^x$$\begin{gathered} In(.0001)=In(\frac{1}{2})^x \\ In(0.0001)=xIn(\frac{1}{2}) \\ x=\frac{In(0.0001)}{In(\frac{1}{2})} \\ x=13.28 \end{gathered}$

It would take 13.28 min for the population of cells to reach 10