Answer:
1044.3 days
Explanation:
Given,
Radius of sphere shaped cells of tumor [tex]= 5[/tex] micrometer
[tex]1[/tex] centimeter [tex]= 10,000[/tex] micrometers
Thus, radius of sphere in centimeters
[tex]= \frac{5}{10,000} \\[/tex]
Volume of a sphere
[tex]= \frac{4}{3} \pi r^{3}[/tex]
Volume of one cell of tumor
[tex]\frac{4}{3} *(3.14)*(\frac{5}{10,000})^{3}\\= {5.23 * 10^{-10}[/tex] centimeter cube
As we know ,
[tex]N(t) = N(0) e^{-kt}\\\\k = \frac{ln2}{35}\\ k = 0.0198 day^{-1}\\[/tex]
Substituting all the given values in above equation, we get -
[tex]0.2 = 5.23 * 10^{-10} * e^{-0.0198*t}\\t = 1044.3[/tex] days
