anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
just tell me is this convergent or divergent
SolomonZelman
  • SolomonZelman
well, 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
  • SolomonZelman
he 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)

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SolomonZelman
  • SolomonZelman
So, lets write this series, and lets diregard the fact that he is to pay some finite loan amount. OK?
anonymous
  • anonymous
is 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.
anonymous
  • anonymous
is divergent
SolomonZelman
  • SolomonZelman
\(\large\color{black}{ \displaystyle a_1=100 }\) \(\large\color{black}{ \displaystyle r=1.1 }\) 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
  • SolomonZelman
The fact that it is a loan is forcing a FINITE series.
SolomonZelman
  • SolomonZelman
If you were to propose a different scenario, such as:
SolomonZelman
  • SolomonZelman
John 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
  • SolomonZelman
this would be more like an INFINITE series scenraio....
anonymous
  • anonymous
ok thanks can u help with another question
SolomonZelman
  • SolomonZelman
ok, but what course is this?
SolomonZelman
  • SolomonZelman
is this geometry or calc?
anonymous
  • anonymous
algebra 2
SolomonZelman
  • SolomonZelman
oh, i see.... go ahead...
SolomonZelman
  • SolomonZelman
((in calc there are more advanced "tools" to use))
anonymous
  • anonymous
The 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
  • SolomonZelman
find f(0). find f(3). find the slope between (0,f(0)) and (3,f(3)).
SolomonZelman
  • SolomonZelman
making sense?
anonymous
  • anonymous
anonymous
  • anonymous
thats the graph
SolomonZelman
  • SolomonZelman
no need for a graph to perform this task, but, it is nice to have one.
SolomonZelman
  • SolomonZelman
do my steps to the solution make sense?
anonymous
  • anonymous
no
SolomonZelman
  • SolomonZelman
Ok, lets do it togther one by one.
anonymous
  • anonymous
so basically your finding slope
SolomonZelman
  • SolomonZelman
yes
SolomonZelman
  • SolomonZelman
did you find f(0) and f(3) ?
SolomonZelman
  • SolomonZelman
f(x) = 2\(^x\)+1
SolomonZelman
  • SolomonZelman
f(0)=2\(^0\)+1=? f(3)=2\(^3\)+1=?
anonymous
  • anonymous
f(3) =7
SolomonZelman
  • SolomonZelman
close
SolomonZelman
  • SolomonZelman
2³ = ?
anonymous
  • anonymous
9
anonymous
  • anonymous
oops
SolomonZelman
  • SolomonZelman
9 is f(3) or just the 2³ part?
anonymous
  • anonymous
2^3
SolomonZelman
  • SolomonZelman
\(2^3=2\times 2 \times 2 \)
SolomonZelman
  • SolomonZelman
=8
anonymous
  • anonymous
f(0) = 1
anonymous
  • anonymous
f(3) = 9
anonymous
  • anonymous
i meant that
SolomonZelman
  • SolomonZelman
yes,
SolomonZelman
  • SolomonZelman
f(3)=9
SolomonZelman
  • SolomonZelman
and f(0)=?
anonymous
  • anonymous
1
SolomonZelman
  • SolomonZelman
no
SolomonZelman
  • SolomonZelman
your function is \(f(x)=2^x+1\)
SolomonZelman
  • SolomonZelman
\(f(0)=2^0+1=?\)
anonymous
  • anonymous
f(0) = 0 + 1
SolomonZelman
  • SolomonZelman
\({\rm C}^0=1\) (for any real number C)
anonymous
  • anonymous
f(0) = 1
SolomonZelman
  • SolomonZelman
\( f(0)=2^0+1=1+1=?\)
anonymous
  • anonymous
2
SolomonZelman
  • SolomonZelman
yes, f(0)=2
anonymous
  • anonymous
Explain how to find the average rate of change between x = 0 and x = 3.
SolomonZelman
  • SolomonZelman
now, 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
  • SolomonZelman
\(\LARGE \color{black}{ \displaystyle {\rm m}=\frac{\color{blue}{{\rm y}_1}-\color{red}{{\rm y}_2}}{\color{green}{{\rm x}_1}-\color{darkgoldenrod}{{\rm x}_2}} }\) 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.
anonymous
  • anonymous
9-2 =7 3-0 =3
SolomonZelman
  • SolomonZelman
yes, so your slope is?
anonymous
  • anonymous
7/3
SolomonZelman
  • SolomonZelman
yup
anonymous
  • anonymous
is that the final answer
SolomonZelman
  • SolomonZelman
yes, that is the final answer for your second question.
anonymous
  • anonymous
so what is the average rate of change again
SolomonZelman
  • SolomonZelman
7/3 :)
SolomonZelman
  • SolomonZelman
slope and average rate of change (in this context) is the same thing.
anonymous
  • anonymous
thanks so much
SolomonZelman
  • SolomonZelman
you are welcome !

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