Question

How can I create a half-life function based on the graph of a logarithmic decay function?

Answer 1

Half-life will be the time it takes for 50% decay. Slope of mass vs. time curve will show this. Might put best-fit line through the data.

Answer 2

I'll post what I have, give me a second.

Answer 3

we were asked to create an experiment to simulate the half-life of a substance, and these are the resulting points. Geogebra assigned them a best- fit exponential function. From there, we are supposed to convert that function into a logarithmic function, and find a decay equation in the form f(x)=A(1/2)^x

Answer 4

in case the picture wont open, the equation that geogebra determined was f(x)=106.38e^(-0.67x)

Answer 5

Presumably x means time.

exp(-0.693) = 0.50 at the x = half-life, T
so 0.693 is the value of x/T

0.67 x = 0.693 x/T

t = 0.693/0.67 = 0.967.

the x you have is nearly in units of half-lives

Answer 6

where did exp(-0.693) come from?

Answer 7

is that just a more accurate number, used instead of e^-0.67?

Answer 8

exp(-0.693) = 1/2

Answer 9

exp(-0.67) = 0.512. Small difference.

Answer 10

alright. How would i convert that into a logarithmic function? i repeatedly get lny=-0.67x+4.667, which is the exact same thing.
It should be the inverse when graphed, correct?

Answer 11

(exponential to logarithmic should be inverse, i mean.)

Answer 12

This should plot as a straight line on semi-log paper, which is
log y = mx + b