Calculating Ant Population Growth Over 10 Days

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The discussion focuses on calculating the growth rate of an ant population over ten days, starting with 65 ants on Day 0 and reaching 161 ants by Day 10. Participants suggest using the formula P=PoR^(t/h) to determine the growth rate, but there is confusion about the variable "h." The conversation emphasizes the need to calculate the number of new ants produced each day, rather than just applying the formula without context. A rough estimate indicates that the population approximately doubles in eight days, providing a benchmark for understanding growth. The goal is to derive ten distinct values representing the ant population for each day.
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Determine the rate of growth in the population of ants for each of the ten days:
Day 0 - 65 ants
Day 1 - 72 ants
Day 2 - 79 ants
Day 3 - 87 ants
Day 4 - 95 ants
Day 5 - 104 ants
Day 6 - 114 ants
Day 7 - 123 ants
Day 8 - 134 ants
Day 9 - 146 ants
Day 10 - 161 antsI believe to solve this you need to use the equation P=PoR^(t/h) where:
P = population
Po = original population
R = rate of growth
t = time
h = time it takes for R to occur.

I've tried using the aforementioned formula, but can't determine what "h" would be? And surely the time would be the number of the day?
 
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What have you tried? You need to show some work before anyone can help you.
 
I think they just want you to calculate how many new ants were produced between Day n and Day n+1 for each of the 11 days.
 
As a quick approximation suggestion, the population about doubles in 8 days.
 
The question asks for ten different values, each corresponding to the count identifying the day number.
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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