Answer
(a) $Q(t) = 100.0124369\cdot e^{-10.00553063~t}$
(b) The current at $~~t = 0.04~s~~$ is $~~-670.6~\mu A$
Work Step by Step
(a) An exponential regression function gives us the following exponential model for the charge:
$Q(t) = 100.0124369\cdot e^{-10.00553063~t}$
(b) We can find the current when $t = 0.04~s$:
$Q(t) = 100.0124369\cdot e^{-10.00553063~t}$
$Q'(t) = (100.0124369)(-10.00553063)\cdot e^{-10.00553063~t}$
$Q'(0.04) = (100.0124369)(-10.00553063)\cdot e^{(-10.00553063)~(0.04)}$
$Q'(0.04) = -670.6~\mu A$
In Example 2.1.2, the current at $~~t = 0.04~s~~$ was estimated to be $~~-670~\mu A~~$ which is very close to the result we found with the exponential model.