Answer:
[tex]A=42, B=-7[/tex]
Step-by-step explanation:
The current function of time is defined as follows:
[tex]I(t)=\frac{dq(t)}{dt}[/tex]
where [tex]q(t)[/tex] is the charge function.
For the given charge function of time [tex]q(t)=6\left( 1-e^{-7t}\right)[/tex] we have the following current function:
[tex]I(t)=\frac{d}{dt} \left(6\left( 1-e^{-7t}\right)\right)=42e^{-7t}[/tex]
In the problem it is proposed that [tex]I(t)=Be^{-At}[/tex].
Examining the expression of [tex]I(t)[/tex] we obtained by deriving [tex]q(t)[/tex] with the expression proposed by the problem and comparing term by term:
[tex]I(t)=Be^{-At}=42e^{-7t}[/tex]
We conclude that [tex]A=-7[/tex] and [tex]B=42[/tex].
