Finding the number of penguins after 7 years

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onesun0000

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I tried to answer this problem.

Jane was studying a penguin colony which had approximately 1000 penguins. Each year 20% die from natural causes. There are an equal number of males and females. One male and one female are a couple and each couple has one chick. How many penguins will be in the colony after 7 years? What formula would you use to determine the number of penguins?

I got around 210. I just used the usual decay formula but I am not sure if this is correct the part ""There are an equal number of males and females. One male and one female are a couple and each couple has one chick." makes me confused. Is that part an unnecessary information? Or it's needed to solve the problem?

[MATH]P=1000(1-0.2)^7[/MATH][MATH]P≈210[/MATH]
 
You don't account for new chicks at all.

Each year we go from [MATH]n(t)[/MATH] to [MATH]\left(n(t)+\dfrac{n(t)}{2}\right)\cdot 0.8 = 1.2 n(t)[/MATH]
[MATH]n(t) = (1.2)^t n(0) = 1000 (1.2)^t,~t \text{ measured in years}[/MATH]
It's a bit more complicated than this because penguins must be entire but this is probably what they are after.
 
onesun0000 said:
I just used the usual decay formula but I am not sure if this is correct the part ""There are an equal number of males and females. One male and one female are a couple and each couple has one chick." makes me confused. Is that part an unnecessary information? Or it's needed to solve the problem?
Click to expand...
The idea behind "There are an equal number of males and females. One male and one female are a couple and each couple has one chick" is that for every two penguins, one new penguin will be born, multiplying the number by 1.5; then deaths multiply the number by 0.8, for a net multiplier of 1.5*0.8 = 1.2. This leads to what Romsek said.
 
Of course this problem is flawed. It does not say how often a couple has a chick. Is it every year, just one for the 1st year or is it random. Also how old does a chick have to be before they can be part of a couple?
 
onesun0000 said:
... but I am not sure if this is correct the part ""There are an equal number of males and females. One male and one female are a couple and each couple has one chick." makes me confused. Is that part an unnecessary information? Or it's needed to solve the problem?
Click to expand...
You are trying to figure out how many penguins there will be in 7 years. Since the chicks (penguins!) add to the size of the colony then you need to count them.
 
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