Question

the number of cells in a tumor doubles every 4.5 months. if the tumor begins with a single cell, how many cells will there be after 2 years? after 3 years?

how may cells will there be after 2 years?

(do not round until the final answer. then round to the nearest whole number as needed.)

how many cells will there be after 3 years?

(do not round until the final answer. then round to the nearest whole number as needed.)

Explanation:

Set up the exponential growth model

Using the Exponential Growth and Doubling Time knowledge points

$$ N(t) = N_0 \cdot 2^{t / d} $$

where \(N_0 = 1\) cell, \(d = 4.5\) months, and \(t\) is measured in months.

Calculate the number of cells after 2 years

Using the Unit Conversion and Exponential Growth knowledge points

$$
LATEXBLOCK0
$$

Calculate the number of cells after 3 years

Using the Unit Conversion and Exponential Growth knowledge points

$$
LATEXBLOCK1
$$

Answer:

Question 1

How may cells will there be after 2 years?
40

Question 2

How many cells will there be after 3 years?
256