Question

number 3 :)

Answer 1

@sunnnystrong

Answer 2

\[f(x)=12500(0.82)^x\]

f(x)= Price of product A ($)
x= Time (Years)

Part A.)
Is f(x) increasing or decreasing? By what percentage?

So, to answer this problem we have to find the decay factor (as f(x) is clearly decreasing)... How would we do that?

Answer 3

Exponential Decay:

\[A=A _{0}b^t\]
0<b<1
A\[A_{0}=initial\]

Answer 4

we would plug in the numbers of years we need to from the grpah provided ?

Answer 5

yes, tho im not sure

Answer 6

Oh sorry... so
We COULD graph the function and look at how the y values change each year and find a percentage
but it is easier to just remember that:

Rate of decay =
(1-b)

Answer 7

If b= 0.82 (from the equation)
What is the rate of decay?

Answer 8

Another picture ^^ This can apply to exponential decay if:
0<b<1***

Answer 9

if only i knew wha that meant ^

Answer 10

lmao im stuid, its 0.82

Answer 11

Oh sorry haha well...
that is just the general form of exponential decay/increase.
Basically:
Our function:\[f(x)=12500(0.82)^x\]
Where 12500= initial starting amount
0.82= Rate
x=time

Our rate of decay is 1-Rate

Answer 12

@ItryMath no...
close.

It'll be 1-0.82

Answer 13

so 0.18 is rate of decay?

Answer 14

Yep :D

Answer 15

okay

Answer 16

LIKE HOW ARE YOU NOT A PROFESSOR ?!?!

Answer 17

sorry caps

Answer 18

@ItryMath lol nahh XD i still have a lot of school ahead of me haha but for the next one:

Can you make a function for exponential decay based on the given table?

Answer 19

imean 12500(0.18)^x

and what do you want to be (your major)

Answer 20

Welll.... 0.18 is the percent increase but overall the DECAY factor is a single value 1-0.18
& computer engineering :D

Answer 21

but that is for the first one.. the second one is different. look carefully at the table.

The initial point is (1, 5600)

Answer 22

percent decrease***^

Answer 23

*Jaw Drops*

Answer 24

whats the first one???

Answer 25

Part A.) We both agreed it's 18% decrease.
Moving on to part B -->

Can you write a function for the given table?

Answer 26

oh okay

Answer 27

sorry my brain stops working around 10 and its 11 rn and i reall am trying lmao but im stupid rn

Answer 28

i dont want you to do all the work even though you seem to be

Answer 29

No it's okay i'm actually just bored at home lol

Answer 30

But it's cool I should let you do it XD

Answer 31

Be my tutor PLEASE i'll pay you big $$$$

Answer 32

$$

Answer 33

no it's okay lol :P

Answer 34

i know the function should be in a(b)^x form so x would be 1 b would be not sure and a is 5600

Answer 35

crying because life just go harder xD

Answer 36

Well, you are right I agree with you.
The function will look something like:

\[A=A _{0}(1-b)^x\]

Where \[A _{0}=initial \]
b=percent of decay
x=time

Answer 37

x=1 b = ?!??!?///????

Answer 38

x doesn't always equal 1... x=time
b=rate of decay.
Basically:
f(1)-f(2)=???
That number/f(1)=b

Answer 39

@ItryMath can you find b? ^^

Answer 40

oh yes of course (back)

Answer 41

2464

Answer 42

sorry took so long ... im in lake tahoe so this obviously isnt my house where everything is set up xD

Answer 43

I mean 1 day i plane to own houses around the world because i hate hotes like hate hate them but that requires math and graphs etc :(

Answer 44

hm... no. try and think about it.
General process:
f(1)-f(2)=???
That number/f(1)=b

Answer 45

-2464

Answer 46

i dont know tbh .....

Answer 47

f(2)=3136
f(1)=5600

5600-3136=2464

2464/5600= 0.44

Answer 48

0.44=percent of decay
So what is the function?

Answer 49

o we divide after -_-

Answer 50

yeah sorry lol
but i feel like you got this. whats the function?

Answer 51

no you dont lmao

Answer 52

5600(0.44)^x

Answer 53

Almost!!!! and yes i do :D

Answer 54

What did we talk about ... there is a percent of decay & a DECAY FACTOR... (1-b)....

Answer 55

(-0.44)

Answer 56

no. b=0.44....
1-0.44 does not equal -0.44

Answer 57

0.56

Answer 58

Yep. Than you pretty much have all of the info you need to answer B confidently (:

Answer 59

OOOMMGGG

Answer 60

WOOOO

Answer 61

You saved me.... you realize that... you would become an awesome doctor xD

Answer 62

okay well imma go to sleep thanks so much!

Answer 63

@ItryMath XD That's very nice! And it is always my pleasure :D

Take care!!

Answer 64

@jim_thompson5910 doesn't product B have the greatest percentage change?

Answer 65

What's the full problem again @ItryMath ?

Answer 66

what percent change did you get for B?

Answer 67

56%

Answer 68

and 18% for A

Answer 69

you should find that 1+r = 0.56

solve for r

Answer 70

1.56

Answer 71

So B right...

Answer 72

1+r = 0.56 does not lead to r = 1.56

try again

Answer 73

it might be helpful to think of `1+r` as `r+1`

Answer 74

oh oops sorry!

Answer 75

-0.44

Answer 76

wait so it isnt 56 %.... its 44

Answer 77

yes so A is decaying by 18% while B is decaying by 44%

Answer 78

in part A, the value of r is

1+r = 0.82
1+r-1 = 0.82-1
r = -0.18

The negative r value indicates decay

Answer 79

so A is decaaying more, is that what you're trying to say @jim_thompson5910

Answer 80

A is decaying by 18% each year
B is decaying by 44% each year

Answer 81

B is decaying more each year

Answer 82

oh so i was right, sorry i got confused lol

Answer 83

@jim_thompson5910 thanks !!!

Answer 84

(:

Answer 85

the negatives probably threw you off

Answer 86

yes