Exponential Growth Test Help Needed | Calc II Summer

AI Thread Summary
A student in a summer Calc II course seeks help with a take-home test on exponential growth, noting the assignment's significant impact on their grade. They mention that while they have covered differential equations, they are still unfamiliar with the topic and prefer their current method of solving the problems. Another participant asks if they understand separation of variables, indicating a potential approach to the problem. The student expresses appreciation for any assistance, highlighting the collaborative nature of the assignment. Overall, the discussion centers on seeking clarification and support for understanding exponential growth concepts.
giant016
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I'm in Calc II for the summer, but for some reason my teacher gave us a take-home test on exponential growth. She said we could work together and such, but the class didn't have time, so I was wondering if somebody could check it for me. It seems pretty straight to me, but it's a large chunk of my grade and my friends/parents wouldn't be of much help, so I would greatly appreciate it if any of you could give it a looking over. My answer sheet is neater, but this has all the work on it. Thanks.
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It couldn't look better really.
 
man why didn't he teach you the DE that this comes from, have you been introduced to differential equations yet?
 
Thanks Dick.

Ice, we have done differentital equations. She said we could do this any way we wanted, and this way I really knew how to do and I'm still a little unfamiliar with DEs.
 
giant016 said:
Thanks Dick.

Ice, we have done differentital equations. She said we could do this any way we wanted, and this way I really knew how to do and I'm still a little unfamiliar with DEs.

do you know how to do separation of variables?
 
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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