I graphed vs. in my TI-83
linear regression yielded the equation
current in mA flowing through a capacitor is discharging over time ms, as shown
i 203 61.14 22.49 6.13 2.49 0.615
t 100 160 210 275 320 390
the graph follows the law of, i = Ie^-t/T (e refers to log, and its to the power of -t/T)
find values for I and T
my solution
log i = log I e ^ -t/T
log i = log I + log e ^ -t/T
log i = -t / T log I
Y = M X + C
i then plot the graph of log of Y against x (shown in attachment)
so - t should = change in log Y / change in x
-t = 3.2 / 392 = 8.16*10^-3
log I = point of intersect 3.2
I = e3.2
I = 24.53
t = 8.16*10^-3
i do this and then put the values into the forumla
24.53e^((8.16*10^-3)/t) = i
but am not getting the correct answers if t is 100 it should be 203 but i get 24.53
any help on where iv gone wrong would be helpful