Question

Question #07b7f

Answer 1

See steps below.

Explanation:

(a) Given expression is `V=V_0cdote^(-t/(RcdotC))`
To make `t` its subject.
Divide both sides with `V_0` and take natural logarithm of both sides.
In the first step we obtain
`V/V_0=e^(-t/(RcdotC))`
In the second step
`ln (V/V_0)=ln e^(-t/(RcdotC))`, eliminating `e`
`ln (V/V_0)=-t/(RcdotC)`, now making `t` its subject
`t=-(RcdotC)cdotln (V/V_0)`, absorbing `-ve " sign in " ln` function
`t=RcdotCcdotln (V_0/V)`.

(b) For the second part follow same steps as above to obtain
`t=lambdacdotln (N_0/N)`