Question

The intensity, Io, of a light source is reduced to I after passing through d meters of fog according to the formula I = Ioe−0.12d. If 1,200 lumens of light are present initially, what is an equivalent expression written as a percentage rate of lumens lost?

Answer 1

Hint: Find the value of e−0.12 on your calculator.

I = 1,200ed
I = 1,200(0.887)d
I = 1,200e0.88d
I = 1,200(0.88)d

Answer 2

@jim_thompson5910 @jagr2713

Answer 3

@Jaynator495

Answer 4

@SolomonZelman can you help with a few questions?

Answer 5

jim can you help with a few of these?

Answer 6

what is the value of `e^(-0.12)` ?

use this calculator if you don't have a calculator with you

http://web2.0calc.com/

Answer 7

0.88692043671

Answer 8

so b yes?

Answer 9

Yes correct

\[\Large \color{red}{e^{-0.12}} \approx \color{red}{0.88692043671712}\]

------------------------------------------------

\[\Large I = I_0 e^{-0.12d}\]

\[\Large I = I_0\left(e^{-0.12}\right)^{d}\]

\[\Large I = I_0\left(\color{red}{e^{-0.12}}\right)^{d}\]

\[\Large I = I_0\left(\color{red}{0.88692043671712}\right)^{d}\]

\[\Large I = I_0*0.887^{d}\]

Then we plug in the initial value \(\Large I_0 = 1200\) to get this final answer

\[\Large I = 1200*0.887^{d}\]

Answer 10

knew it thank you! i need a few more done you have some time?

Answer 11

I'll help with 2 more

Answer 12

great

Answer 13

An automobile is depreciating at 13% per year, every year. A $52,000 car depreciating at this rate can be modeled by the equation V(t) = 52,000(0.87)t. What is an equivalent equation for this vehicle at a daily depreciation and what is it worth (rounded to the nearest thousand dollar) 5 years after purchase?

V(t) = 52,000(0.87)365t, $26,000
V(t) = 52,000(0.9996)t, $52,000
V(t) = 52,000(0.87)start fraction t over 365 end fraction, $52,000
V(t) = 52,000(0.99962)365t, $26,000

Answer 14

13% per 52k?

Answer 15

`An automobile is depreciating at 13% per year`

how much is it depreciating per day?

hint: 365 days in a year

Answer 16

wait is 52k what it is after 5 years? so then i have to split that by 5 correct? and that should give me the per year value?

Answer 17

I don't know what you mean

Answer 18

:o 365 in 52 k?

Answer 19

what is 0.13/365 equal to?

Answer 20

0.00035616438 yes?

Answer 21

one moment

Answer 22

ok take your time.

Answer 23

I don't agree with these answer choices. Can you take a screenshot of the full problem?

Answer 24

mm i can probably attach a file give me a moment.

Answer 25

ok I'll be right back

Answer 26

give me a minute need to re-download my photo album.

Answer 27

hey sorry man can I just send you an email of it?

Answer 28

@jim_thompson5910

Answer 29

@SolomonZelman do you perhaps have a solution for this i think jim has removed himself from this chat for a bit?

Answer 30

ok I'm back now

Answer 31

the "attach file" button doesn't work?

Answer 32

uh no this is a photo from a preview gallary i cant attach this i dont believe.

Answer 33

well the answer is either B or C. The issue is that both answer choices say that the car is worth $52,000 after 5 years, but that's the starting value. The value after 5 years should be much less. So I'm thinking there's a typo which is why I wanted to look directly at the problem in the form of a screenshot.

Answer 34

sorry @jim_thompson5910 my internet went dead ok i checking your stuff now i don see a typo so ill tell you if i find something.

Answer 35

V(t) = 52,000(0.9996)t, $52,000

V(t) = 52,000(0.87)start fraction t over 365 end fraction, $52,000
difference one is fraction of t over 365 one is just t and in the parenthesis the decimals are different too.

Answer 36

If there's an answer choice that has

V(t) = 52,000(0.9996)^t; $26,000

then it would work since plugging t = 5 into V(t) = 52,000(0.9996)^t gives roughly 26,000

Answer 37

but I'm guessing there's a typo that the teacher made

Answer 38

there is an answer that says that lol

Answer 39

thats what D is

Answer 40

well there's a 365 in there though

Answer 41

so second guess is b because it doesn't have the 365?

Answer 42

yeah but it has the 52000 instead of 26000

Answer 43

if only there was a way to combine the answer choices

Answer 44

lol so what would you suggest? I'm not just putting down anything. I would like to know which one it is and how we got to it?

Answer 45

i say your correct about D but why is 265 is set back... i mean you did ask me to use that when i divided.

Answer 46

well it's definitely V(t) = 52,000(0.9996)^t because

0.13/365 = 0.00035616438357

then
1-0.00035616438357 = 0.99964383561643

Answer 47

if 365 is what got you this : (0.9996) then why is it just ^t and not ^t365 after it was used to find that decimal right?

Answer 48

when I plug t = 5 into the original V(t) I get roughly 25917.8878764000 which rounds to $26,000

but when I plug t = 5 into choice D, I get 27143.2375407055 roughly which rounds to $27,000.

Answer 49

So this means D is incorrect yes?

Answer 50

yeah D is a bit off

Answer 51

this problem is just odd, idk why it's like this

Answer 52

so b is the winner? e.e

Answer 53

what about A though?

Answer 54

yeah I guess it's close enough, just that last part is off

Answer 55

ok well i just have one more left now...

Answer 56

A doesn't match either

Answer 57

my last question is -

In a recent stock market downturn, the value of a $1,000 stock is decreasing at 1.6% per month. This situation can be modeled by the equation A(t) = 1,000(0.984)12t, where A(t) is the final amount and t is time in years. Assuming the trend continues, what is the equivalent annual devaluation rate of this stock (rounded to the nearest tenth of a percent) and what is it worth (rounded to the nearest dollar) after 1 year?

82.4% and $824.00
19.2% and $808.00
17.6% and $824.00
80.8% and $808.00

Answer 58

what is 0.984^12 equal to?

Answer 59

0.82402650513

Answer 60

now subtract that from 1

Answer 61

-0.17597349487?

Answer 62

I was thinking

1-0.82402650513947 = 0.17597349486051

Answer 63

multiply 0.17597349486051 by 100% to get

0.17597349486051*100% = 17.597349486051%

that rounds to roughly 17.6%

Answer 64

824 dollars correct?

Answer 65

so 1.6% per month ----> 17.6% per year

Answer 66

yeah after 1 year, the stock is worth $824

Answer 67

k got it.. i know i can do the rest but i doubt they will be right so instead of helping the time can you just check and see if my other two are correct if so then I'm done if not then i have to correct them.