impossible colony of ants
- Thread starter helpche
- Start date
D
Deleted member 4993
Guest
helpche said:
How did you get that?
The answer should be more than 300!
Please show your work.
Hello, helpche!
Denis has the best solution!
But if we must use algebra to solve it . . .
\(\displaystyle \text{Let }a_o\text{ be the original population.}\)
\(\displaystyle \text{Then in }t\text{ months, the population is: }\
(t) \:=\:a_o\,2^{t-1}\)
\(\displaystyle \text{Let }t = n\text{ represent "now": }\;P(n) \:=\:a_o\,2^{n-1} \:=\:10,\!000\;\;{\bf[1]}\)
\(\displaystyle \text{Then 5 months ago: }\(n\!-\!5) \:=\:a_o\,2^{n-6} \:=\:X\;\;{\bf[2]}\)
\(\displaystyle \text{Divide {\bf[2]} by {\bf[1]}: }\;\frac{X}{10,\!000} \;=\;\frac{a_o\,2^{n-6}}{a_o\,2^{n-1}} \quad\Rightarrow\quad \frac{X}{10,\!000} \:=\:2^{-5}\)
\(\displaystyle \text{Therefore: }\;X \;=\;10,\!000\cdot 2^{-5} \;=\;312.5\)
Denis has the best solution!
But if we must use algebra to solve it . . .
\(\displaystyle \text{Let }a_o\text{ be the original population.}\)
\(\displaystyle \text{Then in }t\text{ months, the population is: }\
(t) \:=\:a_o\,2^{t-1}\) \(\displaystyle \text{Let }t = n\text{ represent "now": }\;P(n) \:=\:a_o\,2^{n-1} \:=\:10,\!000\;\;{\bf[1]}\)
\(\displaystyle \text{Then 5 months ago: }\
(n\!-\!5) \:=\:a_o\,2^{n-6} \:=\:X\;\;{\bf[2]}\)\(\displaystyle \text{Divide {\bf[2]} by {\bf[1]}: }\;\frac{X}{10,\!000} \;=\;\frac{a_o\,2^{n-6}}{a_o\,2^{n-1}} \quad\Rightarrow\quad \frac{X}{10,\!000} \:=\:2^{-5}\)
\(\displaystyle \text{Therefore: }\;X \;=\;10,\!000\cdot 2^{-5} \;=\;312.5\)
thanks everyone for your feedback so far! I should have typed in the whole question:
"A colony of 10000 insects doubles in number every month. How many insects were there at each time?
a. 2 months ago b. 5 months ago"
we did get 312.5 by simply dividing in 2, 5 times, but the logic of a .5 insect has my step-son refusing to attempt the question as it doesn't make sense to him. I don't belive the question is the problem, but maybe we're not approaching the question in the right way?
appreciate your help on this!
"A colony of 10000 insects doubles in number every month. How many insects were there at each time?
a. 2 months ago b. 5 months ago"
we did get 312.5 by simply dividing in 2, 5 times, but the logic of a .5 insect has my step-son refusing to attempt the question as it doesn't make sense to him. I don't belive the question is the problem, but maybe we're not approaching the question in the right way?
appreciate your help on this!
D
Deleted member 4993
Guest
if you start with 313 ants,
313, 626, 1252, 2504, 5008, 10016.....
Now teach him about "experimental error" - that is close enough to 10,000, and declare victory.
or may be more palatable answer would be - it was either 312 or 313 (starting point).
313, 626, 1252, 2504, 5008, 10016.....
Now teach him about "experimental error" - that is close enough to 10,000, and declare victory.
or may be more palatable answer would be - it was either 312 or 313 (starting point).