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

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

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

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

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

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

how does that solve the equation I listed above?

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

I can show you the first few steps...

I´m lost sorry, no.

which part are you stuck on?

what to do next

do you understand that you need to find x?

did you follow the reasoning above?

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

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

yes

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

i got -.56

*that

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

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

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

.78

that looks more like it.

is that x?

why would my A be 45?

45(1/2)^.78

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

is that the half life function?

no

oh mah gaaahh. this is tuff

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

in this function t represents the time

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

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

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

*amount

at some point, it decays to half its original value

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

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

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

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

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

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

so note here that I said you need to find the value of x for which:
f(x) = 16

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

regardless of how the function itself is defined

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