The power P in an electrical circuit varies with the time t according to the relationship P = 1 - (1,18^kt), where k is a constant.
After 43 s, the power is 0.83 W. Determine the power P after 60 s. Round off your answer to three value digits.
1 - 1.8^(43k) = 0.83
k = -0.07
So now plug in t=60
Wouldn't k be 0.17?
Nevermind I get it now, thanks!
To determine the power P after 60 seconds, we can use the given relationship P = 1 - (1.18^kt) and the information that at 43 seconds, the power is 0.83 W.
We can substitute t = 43 and P = 0.83 into the equation to find the value of the constant k:
0.83 = 1 - 1.18^(43k)
Rearranging the equation:
1.18^(43k) = 1 - 0.83
1.18^(43k) = 0.17
Taking the logarithm of both sides:
log(1.18^(43k)) = log(0.17)
Using the property of logarithms:
43k * log(1.18) = log(0.17)
Now we can solve for k:
k = log(0.17) / (43 * log(1.18))
Using a calculator, we find:
k ≈ -0.0104
Now we can use the value of k in the equation to find the power P at 60 seconds:
P = 1 - (1.18^(kt))
P = 1 - (1.18^(-0.0104 * 60))
Calculating this, we find:
P ≈ 0.826 W
Therefore, the power P after 60 seconds is approximately 0.826 W.