Logs!!

I need to know the followingg about F(x) = 62.13e^(-0.55x)

•The logarithmic function based on the graphed function.
•A description of what the logarithmic function would look like.
•The half-life function

Thanks!

Question

Logs!!

I need to know the followingg about F(x) = 62.13e^(-0.55x)

•The logarithmic function based on the graphed function.
•A description of what the logarithmic function would look like.
•The half-life function

Thanks!

anonymous · Answer

is the first question asking "what is the inverse of this function?"

anonymous · Answer

No, I graphed points and then I drew a function by connecting them and now I need to know what it would be in terms of log.

anonymous · Answer

then i am afraid i do not understand the question because you have an exponential function, not a logarithmic one

we can find the logarithmic function that is the inverse of this one

anonymous · Answer

Oh, then maybe that is what I need to do, I guess I am supposed to put it intosomething along the lines of               In y = -0.55x + 4.13

anonymous · Answer

ok we can do that

anonymous · Answer

Okay

anonymous · Answer

$$F(x) = 62.13e^{-0.55x} $$ put 
$$x=62.13e^{-0.55y}$$and solve for $y$
divide by 62.13 to get 
$$\frac{x}{62.13}=e^{-0.55y}$$ take the log to get 
$$-.55y=\ln(\frac{x}{62.13})$$  divide by -.55 
now here $-.55=-\frac{55}{100}=-\frac{11}{20}$ so dividing by -.55 is the same as multiplying by $-\frac{20}{11}$ so we get 
$$y=-\frac{20\ln(\frac{x}{62.13})}{11}$$

anonymous · Answer

Thanks!! Also, I need help with the description of the log, Thanks so much!

anonymous · Answer

What it would look like on a graph

anonymous · Answer

if you have the graph of $F$ it would be symmetric with respect to the line $y=x$

anonymous · Answer

Awesome! Thankss!! :)

anonymous · Answer

http://www.wolframalpha.com/input/?i=-11%2F%2820%29ln%28x%2F62.13%29%29+for+x+real

anonymous · Answer

i should say "rotated about the line $y=x$"
yw