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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
 one year ago
 one year ago
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
 one year ago
 one year ago

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andreadesirepenBest ResponseYou've already chosen the best response.0
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?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
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:\[F(0)=45*e^0=45\]
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
what you need to find is the value of x to get half this value
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
i.e. what value of x will give you F(x) = 22.5
 one year ago

andreadesirepenBest ResponseYou've already chosen the best response.0
So it would be, 45(1/2)^22.5 ?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
no, you need to solve the equation:\[22.5=45*e^{0.89x}\]
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
this will give you a value for x for which F(x) is equal to half its initial value
 one year ago

andreadesirepenBest ResponseYou've already chosen the best response.0
i plugged, 45*e^.89 into my calculator and got 18.5. is that right?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
how does that solve the equation I listed above?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
you need to rearrange that equation to get an expression for x
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
I can show you the first few steps...
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
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?
 one year ago

andreadesirepenBest ResponseYou've already chosen the best response.0
I´m lost sorry, no.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
which part are you stuck on?
 one year ago

andreadesirepenBest ResponseYou've already chosen the best response.0
what to do next
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
do you understand that you need to find x?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
did you follow the reasoning above?
 one year ago

andreadesirepenBest ResponseYou've already chosen the best response.0
i understand i need to find x, but i dont understand how
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
If I said:\[12=4x\]then would you be able to find the value of x here?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
good, so now use the same principals to solve this for x:\[\ln(0.5)=0.89x\]
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
tat does not look right to me  please show me your steps so that I can check where you may have made a mistake
 one year ago

andreadesirepenBest ResponseYou've already chosen the best response.0
i divided .5 by .89 or is it the other way around?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
you cannot do that  the lefthandside of the equals sign has \(\ln(0.5)\) not just 0.5
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
so first find the value for \(\ln(0.5)\), then divide that by 0.89
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
that looks more like it.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
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.
 one year ago

andreadesirepenBest ResponseYou've already chosen the best response.0
why would my A be 45?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
In the function given to you, the value of the function when x=0 is 45.
 one year ago

andreadesirepenBest ResponseYou've already chosen the best response.0
is that the half life function?
 one year ago

andreadesirepenBest ResponseYou've already chosen the best response.0
oh mah gaaahh. this is tuff
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
In general you ay have an exponentially decaying function defined as:\[F(x)=Ae^{bt}\]
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
in this function t represents the time
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
and you can see (I hope) that when t=0 F(0)=A
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
so A represents the initial amount  i.e. the amount at the start
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
as time passes, the mount decays and gets less and less
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
at some point, it decays to half its original value
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
so, at that point F(t) = A/2
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
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
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
it represents the amount of time that has to elapse before the amount of material decays to half its original value
 one year ago

andreadesirepenBest ResponseYou've already chosen the best response.0
I understand the process but it tells me that it needs to look like this: A(1/2)^x
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
I don't know where you are getting that from  it makes no sense to me.
 one year ago

andreadesirepenBest ResponseYou've already chosen the best response.0
The halflife of a substance is the time it takes for half of the substance to decay. The exponential function representing halflife is f(x) = A(1/2) where A is the initial amount of the substance and x represents the time for decay. The halflife of the substance will depend on the initial amount of substance you have. In this activity, you will experience this formula in action.
 one year ago

andreadesirepenBest ResponseYou've already chosen the best response.0
I had to use pennies in the beggining if that helps, so i thought that was A, i used 25 pennies.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
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
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
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
 one year ago

andreadesirepenBest ResponseYou've already chosen the best response.0
that´s the function? why doesnt it look like f(x) = A(1/2)^x ?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
it is saying that the VALUE of the function will equal A/2
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
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:\[x=\sqrt{16}=4\]
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
so note here that I said you need to find the value of x for which: f(x) = 16
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
so here we are saying that the VALUE of f(x) should be equal to 16
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
regardless of how the function itself is defined
 one year ago

andreadesirepenBest ResponseYou've already chosen the best response.0
So how will the half life equation of my probelm look? like this f(x) = A/2 ?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
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
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
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
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
I need to go now  it is very late here and I need some sleep  hope you understand this concept better now.
 one year ago
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