Question

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

Answer 1

just tell me is this convergent or divergent

Answer 2

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.....

Answer 3

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)

Answer 4

So, lets write this series, and lets diregard the fact that he is to pay some finite loan amount. OK?

Answer 5

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.

Answer 6

is divergent

Answer 7

\(\large\color{black}{ \displaystyle a_1=100 }\)
\(\large\color{black}{ \displaystyle r=1.1 }\)

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).

Answer 8

The fact that it is a loan is forcing a FINITE series.

Answer 9

If you were to propose a different scenario, such as:

Answer 10

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?

Answer 11

this would be more like an INFINITE series scenraio....

Answer 12

ok thanks can u help with another question

Answer 13

ok, but what course is this?

Answer 14

is this geometry or calc?

Answer 15

algebra 2

Answer 16

oh, i see.... go ahead...

Answer 17

((in calc there are more advanced "tools" to use))

Answer 18

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

Answer 19

find f(0).
find f(3).
find the slope between (0,f(0)) and (3,f(3)).

Answer 20

making sense?

Answer 21

thats the graph

Answer 22

no need for a graph to perform this task, but, it is nice to have one.

Answer 23

do my steps to the solution make sense?

Answer 24

no

Answer 25

Ok, lets do it togther one by one.

Answer 26

so basically your finding slope

Answer 27

yes

Answer 28

did you find f(0) and f(3) ?

Answer 29

f(x) = 2\(^x\)+1

Answer 30

f(0)=2\(^0\)+1=?
f(3)=2\(^3\)+1=?

Answer 31

f(3) =7

Answer 32

close

Answer 33

2³ = ?

Answer 34

9

Answer 35

oops

Answer 36

9 is f(3) or just the 2³ part?

Answer 37

2^3

Answer 38

\(2^3=2\times 2 \times 2 \)

Answer 39

=8

Answer 40

f(0) = 1

Answer 41

f(3) = 9

Answer 42

i meant that

Answer 43

yes,

Answer 44

f(3)=9

Answer 45

and f(0)=?

Answer 46

1

Answer 47

no

Answer 48

your function is
\(f(x)=2^x+1\)

Answer 49

\(f(0)=2^0+1=?\)

Answer 50

f(0) = 0 + 1

Answer 51

\({\rm C}^0=1\) (for any real number C)

Answer 52

f(0) = 1

Answer 53

\( f(0)=2^0+1=1+1=?\)

Answer 54

2

Answer 55

yes, f(0)=2

Answer 56

Explain how to find the average rate of change between x = 0 and x = 3.

Answer 57

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)

Answer 58

\(\LARGE \color{black}{ \displaystyle {\rm m}=\frac{\color{blue}{{\rm y}_1}-\color{red}{{\rm y}_2}}{\color{green}{{\rm x}_1}-\color{darkgoldenrod}{{\rm x}_2}} }\)



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.

Answer 59

9-2 =7
3-0 =3

Answer 60

yes, so your slope is?

Answer 61

7/3

Answer 62

yup

Answer 63

is that the final answer

Answer 64

yes, that is the final answer for your second question.

Answer 65

so what is the average rate of change again

Answer 66

7/3 :)

Answer 67

slope and average rate of change (in this context) is the same thing.

Answer 68

thanks so much

Answer 69

you are welcome !