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anonymous
 one year ago
Medal and FAN
John has taken out a loan for college. He started paying off the loan with a first payment of $100. Each month he pays, he wants to pay back 1.1 times as the amount he paid the month before. . Explain why this series is convergent or divergent
anonymous
 one year ago
Medal and FAN John has taken out a loan for college. He started paying off the loan with a first payment of $100. Each month he pays, he wants to pay back 1.1 times as the amount he paid the month before. . Explain why this series is convergent or divergent

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0just tell me is this convergent or divergent

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1well, just paying 1.1 times the previous payment means that sequence diverges (nothing to even talk about a series). BUT, a loan (I would think so) is some finite amount though, so this situtation with a loan is a bad example.....

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1he won't go into paying more than the loan...... (and this all I am assuming there is no interest, since it is not mentioned here)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1So, lets write this series, and lets diregard the fact that he is to pay some finite loan amount. OK?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a finite limit.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{black}{ \displaystyle a_1=100 }\) \(\large\color{black}{ \displaystyle r=1.1 }\) and this is a perfect geometric series. For geometric series to converge, normally, the folloing mst be true: `r<1` yes correct (disregarding the fact that it's a loan).

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1The fact that it is a loan is forcing a FINITE series.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1If you were to propose a different scenario, such as:

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1John is giving a charity to poor children who stand by the Church. THe first month he gave 100$ and then, every month, he wants to give 1.1 times as much as he gave the previous month. is this series convergent or divergent?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1this would be more like an INFINITE series scenraio....

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok thanks can u help with another question

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1ok, but what course is this?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1is this geometry or calc?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1oh, i see.... go ahead...

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1((in calc there are more advanced "tools" to use))

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The graph of f(x) = 2^x + 1 is shown below. Explain how to find the average rate of change between x = 0 and x = 3

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1find f(0). find f(3). find the slope between (0,f(0)) and (3,f(3)).

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1no need for a graph to perform this task, but, it is nice to have one.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1do my steps to the solution make sense?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Ok, lets do it togther one by one.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so basically your finding slope

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1did you find f(0) and f(3) ?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1f(x) = 2\(^x\)+1

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1f(0)=2\(^0\)+1=? f(3)=2\(^3\)+1=?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.19 is f(3) or just the 2³ part?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(2^3=2\times 2 \times 2 \)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1your function is \(f(x)=2^x+1\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(f(0)=2^0+1=?\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\({\rm C}^0=1\) (for any real number C)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\( f(0)=2^0+1=1+1=?\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Explain how to find the average rate of change between x = 0 and x = 3.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1now, you need to find the slope between (0,f(0)) and (3,f(3)). we know f(3)=9, f(0)=2. SO lets plug this in. ~ you have to find the slope between (0,2) and (3,9)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\LARGE \color{black}{ \displaystyle {\rm m}=\frac{\color{blue}{{\rm y}_1}\color{red}{{\rm y}_2}}{\color{green}{{\rm x}_1}\color{darkgoldenrod}{{\rm x}_2}} }\) where \(\LARGE \color{black}{ \displaystyle {\rm m} }\) is the slope \(\Large\color{black}{ \displaystyle (\color{green}{{\rm x}_1}~,~~\color{blue}{{\rm y}_1}) }\) and \(\Large\color{black}{ \displaystyle (\color{darkgoldenrod}{{\rm x}_2}~,~~\color{red}{{\rm y}_2}) }\) are your two points.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes, so your slope is?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is that the final answer

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes, that is the final answer for your second question.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so what is the average rate of change again

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1slope and average rate of change (in this context) is the same thing.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1you are welcome !
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