anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
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?
asnaseer
  • asnaseer
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:\[F(0)=45*e^0=45\]
asnaseer
  • asnaseer
what you need to find is the value of x to get half this value

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asnaseer
  • asnaseer
i.e. what value of x will give you F(x) = 22.5
anonymous
  • anonymous
So it would be, 45(1/2)^22.5 ?
asnaseer
  • asnaseer
no, you need to solve the equation:\[22.5=45*e^{-0.89x}\]
asnaseer
  • asnaseer
this will give you a value for x for which F(x) is equal to half its initial value
anonymous
  • anonymous
i plugged, 45*e^-.89 into my calculator and got 18.5. is that right?
asnaseer
  • asnaseer
how does that solve the equation I listed above?
asnaseer
  • asnaseer
you need to rearrange that equation to get an expression for x
asnaseer
  • asnaseer
I can show you the first few steps...
asnaseer
  • asnaseer
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?
anonymous
  • anonymous
I´m lost sorry, no.
asnaseer
  • asnaseer
which part are you stuck on?
anonymous
  • anonymous
what to do next
asnaseer
  • asnaseer
do you understand that you need to find x?
asnaseer
  • asnaseer
did you follow the reasoning above?
anonymous
  • anonymous
i understand i need to find x, but i dont understand how
asnaseer
  • asnaseer
If I said:\[12=4x\]then would you be able to find the value of x here?
anonymous
  • anonymous
yes
anonymous
  • anonymous
3
asnaseer
  • asnaseer
good, so now use the same principals to solve this for x:\[\ln(0.5)=-0.89x\]
anonymous
  • anonymous
i got -.56
asnaseer
  • asnaseer
tat does not look right to me - please show me your steps so that I can check where you may have made a mistake
asnaseer
  • asnaseer
*that
anonymous
  • anonymous
i divided .5 by -.89 or is it the other way around?
asnaseer
  • asnaseer
you cannot do that - the left-hand-side of the equals sign has \(\ln(0.5)\) not just 0.5
asnaseer
  • asnaseer
so first find the value for \(\ln(0.5)\), then divide that by -0.89
anonymous
  • anonymous
.78
asnaseer
  • asnaseer
that looks more like it.
anonymous
  • anonymous
is that x?
asnaseer
  • asnaseer
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.
anonymous
  • anonymous
why would my A be 45?
anonymous
  • anonymous
45(1/2)^.78
asnaseer
  • asnaseer
In the function given to you, the value of the function when x=0 is 45.
anonymous
  • anonymous
is that the half life function?
asnaseer
  • asnaseer
no
anonymous
  • anonymous
oh mah gaaahh. this is tuff
asnaseer
  • asnaseer
In general you ay have an exponentially decaying function defined as:\[F(x)=Ae^{-bt}\]
asnaseer
  • asnaseer
in this function t represents the time
asnaseer
  • asnaseer
and you can see (I hope) that when t=0 F(0)=A
asnaseer
  • asnaseer
so A represents the initial amount - i.e. the amount at the start
asnaseer
  • asnaseer
as time passes, the mount decays and gets less and less
asnaseer
  • asnaseer
*amount
asnaseer
  • asnaseer
at some point, it decays to half its original value
asnaseer
  • asnaseer
so, at that point F(t) = A/2
asnaseer
  • asnaseer
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
asnaseer
  • asnaseer
it represents the amount of time that has to elapse before the amount of material decays to half its original value
anonymous
  • anonymous
I understand the process but it tells me that it needs to look like this: A(1/2)^x
asnaseer
  • asnaseer
I don't know where you are getting that from - it makes no sense to me.
anonymous
  • anonymous
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.
anonymous
  • anonymous
I had to use pennies in the beggining if that helps, so i thought that was A, i used 25 pennies.
asnaseer
  • asnaseer
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
asnaseer
  • asnaseer
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
anonymous
  • anonymous
that´s the function? why doesnt it look like f(x) = A(1/2)^x ?
asnaseer
  • asnaseer
it is saying that the VALUE of the function will equal A/2
asnaseer
  • asnaseer
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:\[x=\sqrt{16}=4\]
asnaseer
  • asnaseer
so note here that I said you need to find the value of x for which: f(x) = 16
asnaseer
  • asnaseer
so here we are saying that the VALUE of f(x) should be equal to 16
asnaseer
  • asnaseer
regardless of how the function itself is defined
anonymous
  • anonymous
So how will the half life equation of my probelm look? like this f(x) = A/2 ?
asnaseer
  • asnaseer
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
asnaseer
  • asnaseer
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
asnaseer
  • asnaseer
I need to go now - it is very late here and I need some sleep - hope you understand this concept better now.

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