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IgorLugansk [536]
3 years ago
13

Suppose the cells of a tumor are idealized as spheres each with a radius of 5 mum ​(micrometers). The number of cells has a doub

ling time of 35 days. Approximately how long will it take a single cell to grow into a​ multi-celled spherical tumor with a volume of 0.2 cmcubed ​(1 cmequals​10,000 mu​m)
Biology
1 answer:
loris [4]3 years ago
5 0

Answer:

1044.3 days

Explanation:

Given,

Radius of sphere shaped cells of tumor = 5 micrometer

1 centimeter = 10,000 micrometers

Thus, radius of sphere in centimeters

= \frac{5}{10,000} \\

Volume of a sphere

= \frac{4}{3} \pi r^{3}

Volume of one cell of tumor

\frac{4}{3} *(3.14)*(\frac{5}{10,000})^{3}\\= {5.23 * 10^{-10} centimeter cube

As we know ,

N(t) = N(0) e^{-kt}\\\\k = \frac{ln2}{35}\\ k = 0.0198 day^{-1}\\

Substituting all the given values in above equation, we get -

0.2 = 5.23 * 10^{-10} * e^{-0.0198*t}\\t = 1044.3 days

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