Question

number 5 :)

Answer 1

@Seratul

Answer 2

@DanJS

Answer 3

What do you need help with??

Answer 4

#5? a,b,c?

Answer 5

@DanJS yes

Answer 6

do you know the difference in linear and exponential equation?

Answer 7

y=mx+b
y=A*b^x

Answer 8

yes

Answer 9

linear model has a constant slope, or change in values, you see option2 is linear since it increases by 100 each time

Answer 10

a exponential will change by some multiple value each time, you can see from the ratios
1210/1100 = 1.1
1331/1210 = 1.1
this is exponential , the multiplier is 1.1

Answer 11

oh yes i do

Answer 12

can be used to describe the value of the investment after a fixed number of years using option 1 and option 2? Explain your answer.

Answer 13

i copy and paste from question

Answer 14

part A

Answer 15

well, option A wont be able to be constant but option B should be constant right

Answer 16

yes, option B is linear, you can use two points from the table to get the equation for the line

Answer 17

how?

Answer 18

(1 , 1100) and (2 , 1200)

m=100

y - 1100 = 100*(x - 1)
y - 1100 = 100x - 100
y = 100x + 1000

Answer 19

oooooh

Answer 20

okay so i think we answered part A , right >\?

Answer 21

did we answer everything it was asking tho?

Answer 22

okay so we got 1 fnction for B ,so now for A

Answer 23

a) (copied from what i typed above)
--- linear model has a constant slope, or change in values, you see option2 is linear since it increases by 100 each time,
---a exponential will change by some multiple value each time, you can see from the ratios 1210/1100 = 1.1
1331/1210 = 1.1
this is exponential , the multiplier is 1.1

Answer 24

same way right?

Answer 25

Option A is not linear, it increases by a multiple of 1.1 each time, not a constant value

Answer 26

Part A is everything you just copied ?

Answer 27

yes i know but it says write a function at least once for each option

Answer 28

general exponential equation

y = A*b^x

initial value A, multiplier base b

Answer 29

i've seen that but idk what to do with it atm

Answer 30

wait so A=1100 and B= 1.1 (like you said)

Answer 31

you need to figure out the values for A and b
y = A*b^x
you have 3 points (x,y) given on the table, you can use them in the equation

Answer 32

right b=1.1, that is the common multiplier

y = A*(1.1)^x

Answer 33

you can use one of the points (x,y) to get the value for A,

using the first point (1,1100)

y = A*1.1^x

1100 = A*(1.1)^1

Answer 34

so how do we get A?

Answer 35

divid 1100 by 1.1?

Answer 36

\[\large y=A*(1.1)^x\]

yeah just put in a point value for x and y, and solve for A

Answer 37

so we just finished part B correct?

Answer 38

yeah
y=1000*1.1^x

Answer 39

okay part C:

Answer 40

they want it as a function y=f(n)

f(n) = 1000*1.1^n
f(n) = 100n + 100

Answer 41

do i use both or one of them? or the one which produces more profit

Answer 42

they want n=20 years, put that in for both options..

Answer 43

The exponential will at some point in time become the better option. The exponential will give larger and larger increases in investment as the years get larger. Each year the current amount is multiplied by 1.1, and the amount keeps growing each year and so the increases will also grow each year.
as opposed to the linear option, this one just increases by the same 100 each year.

Answer 44

So is olve for option B with the function and explain thats it better than Option A, correct @DanJS

Answer 45

This is what you got for the equations.

Option A -- > f(n) = 1000*1.1^n

Option B -- > f(n) = 100n + 100

Answer 46

The last part asks about the values at 20 years, n=20

Option A -- > f(20) = 1000*1.1^20 = 6727.5
Option B -- > f(20) = 100*20 + 1000 = 3000

Answer 47

and then i explain which one is better and why right

Answer 48

@DanJS

Answer 49

im not sure what to write for part B..

Answer 50

you just write the equations, and explain one is exponential and one is linear, like above

Answer 51

f(n) = 100n + 100 how do we have a intial value of 100? do you mean 1100?

Answer 52

@DanJS

Answer 53

wait whats the original function for option 1 and option 2 .. something doesnt make sense

Answer 54

@sunnnystrong can you help me explain part B?

Answer 55

that was mistyped once, sorry,

f(n)=100n + 1000

Answer 56

where did you get 1000?

Answer 57

go back through the whole thread again

Answer 58

and why isnt it like 100^n

Answer 59

Hmmmm...
well it looks like you already did the work with @DanJS but
\[f(n)=100n + 1000 \]
\[f(n)=1000(1.1)^n \]

Answer 60

i dont understand why 100n and not 100^n

Answer 61

Ohh ... okay well let me see if I can explain haha
As you can see.. Option two is increasing at a constant rate. As @DanJS said...
Therefor it isn't 100^n

Answer 62

oh

Answer 63

Option 2 is an arithmetic sequence. Each new term is 100 more than the previous term.
What about Option 1? Note that the 2nd increase is greater than the 1st increase. This is typical of exponential growth functions.