Question 1089648
.
In the early steps of SARS epidemic in China, {{{highlight(cross(thry))}}} there were 100 persons infected. {{{highlight(cross(that))}}} Then each day the number {{{highlight(cross(increase))}}} increases by 5%. 
After how many days would 500 persons be affected?

Its my problem it Gen Math 11th grade. 
~~~~~~~~~~~~~~~~~


I assume that the condition means  "Then each day the number of affected increases by 5%"


<pre>
I made this table using MS EXcel in my computer.

day    N of people infected:  {{{a[n+1]}}} = {{{1.05*a[n]}}} = {{{100*1.05^(n-1)}}}

1	100.00
2	105.00
3	110.25
4	115.76
5	121.55
6	127.63
7	134.01
8	140.71
9	147.75
10	155.13
11	162.89
12	171.03
13	179.59
14	188.56
15	197.99
16	207.89
17	218.29
18	229.20
19	240.66
20	252.70
21	265.33
22	278.60
23	292.53
24	307.15
25	322.51
26	338.64
27	355.57
28	373.35
29	392.01
30	411.61
31	432.19
32	453.80
33	476.49
34	500.32
35	525.33
36	551.60


If you and your teacher accept it, then OK.

Somebody can criticize me for that my table contains non-integer numbers.


OK, then let somebody will prepare better solution.
</pre>

On geometric progressions, see the lessons in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Geometric-progressions.lesson>Geometric progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/The-proofs-of-the-formulas-for-geometric-progressions.lesson>The proofs of the formulas for geometric progressions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Problems-on-geometric-progressions.lesson>Problems on geometric progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Word-problems-on-geometric-progressions.lesson>Word problems on geometric progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/One-characteristic-property-of-geometric-progressions.lesson>One characteristic property of geometric progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Solved-problems-on-geometric-progressions.lesson>Solved problems on geometric progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Fresh-sweet-and-crispy-problem-on-arithmetic-and-geometric-progressions.lesson>Fresh, sweet and crispy problem on arithmetic and geometric progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Sequences-and-series/Mathematical-induction-and-geometric-progressions.lesson>Mathematical induction and geometric progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Mathematical-induction-for-sequences-other-than-arithmetic-or-geometric.lesson>Mathematical induction for sequences other than arithmetic or geometric</A>



Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic <U>"Geometric progressions"</U>.