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The voltage across a charged capacitor measured in Volts is given by V(t) = 4(2.72)^{\frac{-t}{2} } where t is measured in seconds since the current was removed. Include at least three decimal places in all your answers.
a. What is the voltage after 2 seconds?

b. What is the 1-second growth factor?

c. When will the voltage be 1 Volt?

d. When will the voltage be x Volts? (Your answer should be an exact expression with x in it)



Sagot :

GTLUVSUidn
So first you plug 2 in for t
4(2.72)^(-2/2)
4/2.72 (because the simplified exponent is -1)
divide and that's your answer.

Next you plug 1 in for t
4(2.72)^(-1/2)
4/sqrt(2.72) (because -1/2 as an exponent is 1/sqrt(x))
plug that into a calculator and that's your answer

For c, you plug 1 in for V(t).
1=4(2.72)^(-t/2)
1/4=2.72^(-t/2)
Here is where I get stuck because I haven't done logarithms in a year and forget how to do them but I know that's what you have to do for this problem.

In the last problem you plug x in for V(t) and I'd assume go about solving it the same as c. Sorry I couldn't be of more help.
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