Precalc Question! finding one second growth factor?

Question

The voltage across a charged capacitor measured in Volts is given by V(t)=4(2.72)^(-t/2) where t is measured in seconds since the current was removed. What is the 1-second growth factor? When will the voltage be x Volts? (answer should be an exact expression with x in it) I found the voltage after 2 seconds which is 1.470588235 volts. I also found when the voltage will be 1 volt which is 2.770837884 seconds. 

Answer 1

Hi Alissa,

I haven't heard of the term 1-second growth factor before, but from general knowledge of exponential growth and decay equations I would expect to describe it like this: the multiplier by which the total amount changes each second. If that's true, then it would be
1SGF = 2.72^-t/2 = 2.72^-1/2

The second part of the question you'll answer in the same way that you got the time until it reached 1 volt. Set the total voltage equal to x, and solve for t.
x = 4(2.72)^-t/2