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 2 years 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
 2 years 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

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andreadesirepen
 2 years ago
Best ResponseYou've already chosen the best response.0HELP! 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
 2 years ago
Best ResponseYou've already chosen the best response.1if:\[F(x)=45e^{.89x}\]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
 2 years ago
Best ResponseYou've already chosen the best response.1what you need to find is the value of x to get half this value

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1i.e. what value of x will give you F(x) = 22.5

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

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

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

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

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1how does that solve the equation I listed above?

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1you need to rearrange that equation to get an expression for x

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1I can show you the first few steps...

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1so, 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?

andreadesirepen
 2 years ago
Best ResponseYou've already chosen the best response.0I´m lost sorry, no.

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1which part are you stuck on?

andreadesirepen
 2 years ago
Best ResponseYou've already chosen the best response.0what to do next

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1do you understand that you need to find x?

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1did you follow the reasoning above?

andreadesirepen
 2 years ago
Best ResponseYou've already chosen the best response.0i understand i need to find x, but i dont understand how

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

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

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

andreadesirepen
 2 years ago
Best ResponseYou've already chosen the best response.0i divided .5 by .89 or is it the other way around?

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1you cannot do that  the lefthandside of the equals sign has \(\ln(0.5)\) not just 0.5

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1so first find the value for \(\ln(0.5)\), then divide that by 0.89

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1that looks more like it.

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1yes  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.

andreadesirepen
 2 years ago
Best ResponseYou've already chosen the best response.0why would my A be 45?

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1In the function given to you, the value of the function when x=0 is 45.

andreadesirepen
 2 years ago
Best ResponseYou've already chosen the best response.0is that the half life function?

andreadesirepen
 2 years ago
Best ResponseYou've already chosen the best response.0oh mah gaaahh. this is tuff

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

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1in this function t represents the time

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1and you can see (I hope) that when t=0 F(0)=A

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1so A represents the initial amount  i.e. the amount at the start

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1as time passes, the mount decays and gets less and less

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1at some point, it decays to half its original value

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

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1now, 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
 2 years ago
Best ResponseYou've already chosen the best response.1it represents the amount of time that has to elapse before the amount of material decays to half its original value

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

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1I don't know where you are getting that from  it makes no sense to me.

andreadesirepen
 2 years ago
Best ResponseYou've already chosen the best response.0The 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.

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

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1where 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
 2 years ago
Best ResponseYou've already chosen the best response.1what 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

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

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1it is saying that the VALUE of the function will equal A/2

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

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

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1regardless of how the function itself is defined

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

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1the 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
 2 years ago
Best ResponseYou've already chosen the best response.1this 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
 2 years ago
Best ResponseYou've already chosen the best response.1I 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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