Radioactive decay
find the half-life of a radioactive material for which 99.57% of the initial amount remains after 1 year.

t=160.82 years

Step-by-step explanation:

exponential decay function is

If initial amount A_1 is 100 then material remaining is 99.57

divide both sides by 100, question says 1 year so t=1

take ln on both sides

k=-.00431  

t=1, A= 50 remaining (half life)

divide both sides by 100

take ln on both sides

t=160.82 years

see below

step-by-step explanation:

x+2> 6

subtract 2 from each side

x+2-2 > 6-2

x > 4

there is an open circle at 4 since is it is greater than and the line goes to the right