Question

The voltage V across a charged capacitor is given by V(t) = 2e^-0.16t volts, where t is in seconds

(A) what is the voltage V(5) after 5 seconds? Find the time t when the voltage will be 1 volt

Enter your answers to two decimal places

V(5) approximately ___________ volts

t approximately ___________ sec

(B) By what percent B does the voltage decrease each second ?

Enter your answer to two decimal places

B approximately ________ %

Answer 1

if t = 5
2 e^-(.16*5)=2 e^-.8 = 2/e^.8 = .899 = .90 volts

1 = 2 e^-(.16t)
ln .5 = -.16 t
t = 4.33 seconds

at 0 sec V = 2
at 5 seconds V = .90

V = Vi (r)^t
.9 = 2 r^5
.45 = r^5
log .45 = 5 log r
r = .852
so every second multiply by .85
so decreases by 15% every second