Question

How do I write a half life function of this info?
F(x)=45e^-.89x
y=45e^-.89x
y/45 = e^(-.89x)
in y/45 = In e^(-.89x)
in y - in 45 = in e^-.89x
in y = in e^-.89x+3.81
in y = -.89x+3.81

Answer 1

HELP! It says it should look like this: F(x)=A(1/2)^x. Where A is the initial amount of the substance and x represents the time for decay. I have A, it´s 25. How do i find x?

Answer 2

if:\[F(x)=45e^{-.89x}\]then the value of F(0) will tell you how much the initial amount is equal to. In this case it would be:\[F(0)=45*e^0=45\]

Answer 3

what you need to find is the value of x to get half this value

Answer 4

i.e. what value of x will give you F(x) = 22.5

Answer 5

So it would be, 45(1/2)^22.5 ?

Answer 6

no, you need to solve the equation:\[22.5=45*e^{-0.89x}\]

Answer 7

this will give you a value for x for which F(x) is equal to half its initial value

Answer 8

i plugged, 45*e^-.89 into my calculator and got 18.5. is that right?

Answer 9

how does that solve the equation I listed above?

Answer 10

you need to rearrange that equation to get an expression for x

Answer 11

I can show you the first few steps...

Answer 12

so, starting with:\[22.5=45*e^{-0.89x}\]we divide both sides by 45 to get:\[0.5=e^{-0.89x}\]then take logs of both sides to get:\[\ln(0.5)=-0.89x\]can you do the rest?

Answer 13

I´m lost sorry, no.

Answer 14

which part are you stuck on?

Answer 15

what to do next

Answer 16

do you understand that you need to find x?

Answer 17

did you follow the reasoning above?

Answer 18

i understand i need to find x, but i dont understand how

Answer 19

If I said:\[12=4x\]then would you be able to find the value of x here?

Answer 20

yes

Answer 21

3

Answer 22

good, so now use the same principals to solve this for x:\[\ln(0.5)=-0.89x\]

Answer 23

i got -.56

Answer 24

tat does not look right to me - please show me your steps so that I can check where you may have made a mistake

Answer 25

*that

Answer 26

i divided .5 by -.89 or is it the other way around?

Answer 27

you cannot do that - the left-hand-side of the equals sign has \(\ln(0.5)\) not just 0.5

Answer 28

so first find the value for \(\ln(0.5)\), then divide that by -0.89

Answer 29

.78

Answer 30

that looks more like it.

Answer 31

is that x?

Answer 32

yes - you can double check that you have the right value for x by substituting it into your original equation:\[F(x)=45e^{-.89x}\]and see if you get roughly 22.5 as the answer.

Answer 33

why would my A be 45?

Answer 34

45(1/2)^.78

Answer 35

In the function given to you, the value of the function when x=0 is 45.

Answer 36

is that the half life function?

Answer 37

no

Answer 38

oh mah gaaahh. this is tuff

Answer 39

In general you ay have an exponentially decaying function defined as:\[F(x)=Ae^{-bt}\]

Answer 40

in this function t represents the time

Answer 41

and you can see (I hope) that when t=0 F(0)=A

Answer 42

so A represents the initial amount - i.e. the amount at the start

Answer 43

as time passes, the mount decays and gets less and less

Answer 44

*amount

Answer 45

at some point, it decays to half its original value

Answer 46

so, at that point F(t) = A/2

Answer 47

now, since we know that:\[F(t)=Ae^{-bt}\]then we can replace F(t) by A/2 to get:\[\frac{A}{2}=Ae^{-bt}\]divide both sides by A to get:\[\frac{1}{2}=e^{-bt}\]take logs of both sides to get:\[\ln(0.5)=-bt\]divide both sides by -b to get:\[t=-\frac{\ln(0.5)}{b}\]this is what the half life is

Answer 48

it represents the amount of time that has to elapse before the amount of material decays to half its original value

Answer 49

I understand the process but it tells me that it needs to look like this: A(1/2)^x

Answer 50

I don't know where you are getting that from - it makes no sense to me.

Answer 51

The half-life of a substance is the time it takes for half of the substance to decay. The exponential function representing half-life is f(x) = A(1/2) where A is the initial amount of the substance and x represents the time for decay. The half-life of the substance will depend on the initial amount of substance you have. In this activity, you will experience this formula in action.

Answer 52

I had to use pennies in the beggining if that helps, so i thought that was A, i used 25 pennies.

Answer 53

where you wrote:

f(x) = A(1/2)

that corresponds to what I said above when I said that at its half life:

so, at that point F(t) = A/2

Answer 54

what this is saying is that when the material (whatever it may be) reaches its half life, then the value of the function f(x) will be equal to HALF the value of f(0).

and we know that f(0) = A

so, at its half life, f(x) = A/2

Answer 55

that´s the function? why doesnt it look like f(x) = A(1/2)^x ?

Answer 56

it is saying that the VALUE of the function will equal A/2

Answer 57

e.g. if I had a function defined as:\[f(x)=x^2\]and I asked you to find the value of x for which f(x) = 16, then you would do:\[16=x^2\]therefore:\[x=\sqrt{16}=4\]

Answer 58

so note here that I said you need to find the value of x for which:

f(x) = 16

Answer 59

so here we are saying that the VALUE of f(x) should be equal to 16

Answer 60

regardless of how the function itself is defined

Answer 61

So how will the half life equation of my probelm look? like this f(x) = A/2 ?

Answer 62

the HALF LIFE is defined as the point at which the VALUE of the function is equal to half its initial value - i.e. the point at which f(x) = A/2

Answer 63

this is not stating that the FUNCTION definition is f(x) = A/2
instead it is stating that the VALUE of f(x) = A/2
and you need to find a suitable x for this to be true

Answer 64

I need to go now - it is very late here and I need some sleep - hope you understand this concept better now.