Question

How do you set up this Exponential Equation?

Answer 1

I think it is \[P(t)=Pe ^{(1/3)(30)}\]
I am not sure

Answer 2

A radioactive frog hops out of a pond full of nuclear waste in Oak Ridge,
TN. If its level of radioactivity declines to 1/3 of the original value in 30 days, when will
its level of radioactivity reach 1/100 of its original value?

Answer 3

http://curvebank.calstatela.edu/radiodecay/decayeq.jpg

Answer 4

so yes you are correct

Answer 5

but the tricky part is that we don't have any clear original mass number.

Answer 6

so what would we do @3abf6277

Answer 7

It's number 7 but I do not understand http://www.math.rutgers.edu/~sferry/MA135F14/135-f14/Final2008.pdf

Answer 8

Ah I can explain

Answer 9

so first we have some data: 1/3 of the original value in 30 days.

Answer 10

yes

Answer 11

this is essentially a point on the graph we can plug into the question. after 30 days the FINAL value of the mass is 1/3 its original value. This is decaying at a rate that is NOT given, k which we can solve for

Answer 12

So we can leave\[P = P e^((-k)(30))\] after we substitute 30 in for the time

Answer 13

so its 1/3P

Answer 14

yup on the left side

Answer 15

then what

Answer 16

Because both P's in this case are the original value, except that on the left side, it is 1/3(P), we can cancel the P's

Answer 17

I think you can do the rest, theres only one variable left.

Answer 18

tell me what you get as k

Answer 19

then the ln in raised

Answer 20

exactly you ln both sides to get rid of the e, and its simple algebra after that

Answer 21

ln(1/3)/30

Answer 22

I love you

Answer 23

OH but hey remember, that its exponential decay, NOT exponentialy growth

Answer 24

which is why there it is -k not +k

Answer 25

wait so

Answer 26

why does the person flip the ln(1/100)

Answer 27

ok well i'm assuming you get everythign up to that point, its the same excercise essentially we did in the right side of that page. whenever you divide logarithmic equations, you divide them

Answer 28

lemme get a chart of log rules

Answer 29

I know but he flipped the 1/100 for no reason

Answer 30

http://www.purplemath.com/modules/logrules.htm

Answer 31

@3abf6277 it didnt answer my question

Answer 32

so taking that example log(1/100) is also equal to log(100^-1)

Answer 33

look at the bottom of the page i linked it shows the expansion rule

Answer 34

that -1 can come out to the front

Answer 35

seeing as (1/100) = (100)^-1

Answer 36

on the first page right?

Answer 37

nvm i get it

Answer 38

so the power rule is it comes to the front

Answer 39

exactly!

Answer 40

yea in calculus remembering all those exponential rules and log rules will help alot

Answer 41

you probably already know this but: http://tutorial.math.lamar.edu/ are so good. they helped me a lot when the prof or textbook wasnt

Answer 42

thanks I never heard of this @3abf6277 i use khan academy

Answer 43

oh dude this guys notes too: http://patrickjmt.com/