The integrated rate law allows chemists to predict the reactant concentration after a certain amount of time,

The integrated rate law allows chemists to predict the reactant concentration after a certain amount of time, or the time it would take for a certain concentration to be reached.

The integrated rate law for a first-order reaction is: [A] = [A]e^-kt}

Now say we are particularly interested in the time it would take for the concentration to become one-half of its initial value. Then we could substitute \rm [A]\2 for [A] and rearrange the equation to:
t1/2 = 0.693/k
This equation calculates the time required for the reactant concentration to drop to half its initial value. In other words, it calculates the half-life.

Question 1 is What is the half-life of a first-order reaction with a rate constant of 5.60×10^−4 s^-1?
answer: 1240 s

Question 2 is What is the rate constant of a first-order reaction that takes 249 seconds for the reactant concentration to drop to half of its initial value?
answer : 2.79×10−3 s^-1

NEED HELP ON QUESTION 3: A certain first-order reaction has a rate constant of 1.60×10^−3 s^-1. How long will it take for the reactant concentration to drop to 1/8 of its initial value?

t1/2 = 0.693 / 2.79x10^-3 = 248.39 s
1/2 after 248.39 s
1/4 after 496.78 s
1/8 after 745.17 s

ln(8/1) = 2.79x10^-3 x t
t = 745 s