Mathematics: Suppose that the number of cells in a tumor doubles every 5 months. considering that the tumor begins with a single cell, answer the following: how many cells will there be after 3 years? 5 years?

Suppose that the number of cells in a tumor doubles

Ответ:

coontcakes

17.01.2022

Let's call a 5-month period a "pent", so the conversion from years to pents is 1 year for every 2.2 pents.

Then

$3\text{ years}\times\dfrac{2.2\text{ pents}}{1\text{ year}}=6.6\text{ pents}$

and

$5\text{ years}\times\dfrac{2.2\text{ pents}}{1\text{ year}}=11\text{ pents}$

Now, if the number of cells doubles every pent, and if C_n

denotes the number of cells after

pents, then the number of cells is modeled recursively by

$C_{n+1}=2C_n$

starting with C_0=1

.

Solving explicitly for C_n

, you arrive at

$C_{n+1}=2C_n=2^2C_{n-1}=2^3C_{n-2}=\cdots=2^{n+1}C_0$

or,

C_n=2^nC_0=2^n

So, after 6.6 pents (3 years), you should expect the number of cells to grow to about $2^{6.6}\approx97$ . After 11 pents (5 years), you should find $2^{11}=2048$ cells.

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Ответ:

salvadorjr1226p4zkp3

13.02.2020

Mathematics

D:Length side LM over length of side MN equals length of side XY over length of side XZ.

Step-by-step explanation:

We are given that two triangles LMN and XYZ are similar.

We have to find the not necessarily true information about given triangles.

We know that when two triangles are similar then their corresponding angles are congruent and the ratio of corresponding sides of two triangles are equal.

$\triangle LMN\sim \triangle XYZ$