After 70.0 min. 34% of a compound has decomposed. What is the half-life of this reaction assuming first order

After 70.0 min. 34% of a compound has decomposed. What is the half-life of this reaction assuming first order kinetics?

please explain step by step

Thank you so much!

ln(amount/initialAmount) = -rateConstant * t

We don't know the rate constant yet.

Since 34% decomposed, 66% is left. 66% = 66/100 = .66
We can use this to figure out the value of the rate constant.

ln (.66) = -rateConstant * 70.0min
rateConstant = .00593593491 / min

We want to know how long it will take for 50% to decompose, or 50% to remain. 50% = 50/100 = .5
ln(.5) = -.00593593491 / min * t
t = 116.771357947 min

Answer with proper significant figures: 120 min