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The number of cells in a tumor doubles every 2.5 months. If the tumor begins with a single cell, how many cells will there be after 2 years? after 5 years?Question content area bottomPart 1How may cells will there be after 2 years?  (Do not round until the final answer. Then round to the nearest whole number as needed.)

Sagot :

Solution.

The problem is an exponential growth problem (Because The number of cells in the tumor doubles every 2.5 months)

The formula for exponential growth is

In the problem given,

a = 1

r = 2

(i) After 2 years, that is ( 2 x 12 months = 24 months)

t = 24/2.5 = 9.6

[tex]\begin{gathered} f(9.6)=1(1+2)^{9.6} \\ =1(3)^{9.6} \\ =38050.822 \\ =38,050(nearest\text{ whole number\rparen} \end{gathered}[/tex]

The number of cell that will be after 2 years = 38,050 cells (nearest whole number)

(ii) After 5 years

5 years = 5 x 12 months = 60 months

t = 60/2.5 = 24

[tex]\begin{gathered} f(24)=1(1+2)^{24} \\ =3^{24} \\ =282,429,536,481 \end{gathered}[/tex]

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