For the half life: the half life is the solution

You want to solve for t so need to isolate the e by dividing the coefficient out, then take the ln of both sides. So a/2 divided by a gives you 1/2, meaning 1/2=e^-7.633t Now ln(1/2)=ln(e^-7.633t). Use your power rule to bring the exponent down in front so ln(1/2)=(-7.633t)(ln(e). Remember that ln(e)=1 so ln(1/2)=(-7.633t)(1). Now divide both sides by -7.633 so that ln(2)/-7.633 = t. Plug this into your calculator to get your answer and don't forget to round to three decimal places for this particular question.

The first one is 2/3the second is 1/160the third is 4/125