We are asked to find the half-life of the reaction from the diagram if it follows first-order kinetics.

The integrated rate law for a first-order reaction is as follows:

$\overline{){\mathbf{ln}}{\mathbf{}}{{\mathbf{\left[}}{\mathbf{N}}{\mathbf{\right]}}}_{{\mathbf{t}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{\mathbf{-}}{\mathbf{kt}}{\mathbf{}}{\mathbf{+}}{\mathbf{}}{\mathbf{ln}}{\mathbf{}}{{\mathbf{\left[}}{\mathbf{N}}{\mathbf{\right]}}}_{{\mathbf{0}}}}$

where:

**[N]**** _{t}** = concentration of reactants at time t

**k** = decay constant

**t** = time

**[N]**** _{0}** = initial concentration

Given the following diagrams at t = 0 and t = 30, what is the half-life of the reaction if it follows first-order kinetics?

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