QuestionThe number of cells in a tumor doubles every 3.5 months. If the tumor begins with a single cell, how many cells will there be after 3 years? after 4 years?
How may cells will there be after 3 years?
(Do not round until the final answer. Then round to the nearest whole number as needed.)
Studdy Solution
STEP 1
What is this asking? If a tumor starts with one cell and doubles in size every 3.5 months, how many cells will there be after 3 years and 4 years? Watch out! Don't forget to convert years to months and be careful with how many times the cells double!
STEP 2
1. Convert years to months
2. Calculate the number of doublings
3. Calculate the number of cells
STEP 3
There are 12 months in a year, so 3 years is **months**!
STEP 4
Similarly, 4 years is **months**!
STEP 5
The cells double every 3.5 months, and we have 36 months total.
So, in 3 years, the cells double **times**.
STEP 6
For 4 years (48 months), the cells double **times**.
STEP 7
We start with 1 cell.
After the first doubling, we have cells.
After the second doubling, we have cells, and so on.
This is just like raised to the power of the number of doublings!
So, after approximately 10.29 doublings, we have cells.
STEP 8
Similarly, after approximately 13.71 doublings, we'll have cells.
STEP 9
After 3 years, there will be approximately **1156** cells (rounded to the nearest whole number).
After 4 years, there will be approximately **11194** cells (rounded to the nearest whole number).
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