Question 1199250
half life is 125 days.
formula becomes .5 = g ^ 125
g is the growth rate per day.
take the 125th root of both sides of the equation to get:
.5 ^ (1/125) = g
solve for g to get:
g = .9944701687
that's the daily growth rate.
if the radioactive substance starts at 1 and you want 82% to decay, then the remainder would be 1 - .82 * 1 = .18.
the formula decays from 1 to .18 in x days.
the formula becomes .18 = 1 * .9944701687 ^ x
simplify to get .18 = .9944701687 ^ x
take the log of both sides of the equation to get:
log(.18) = log(.9944701687 ^ x)
this becomes log(.18) = x * log(.9944701687)
solve for x to get:
x = log(.18) / log(.9944701687) = 309.2413985 days.
that's pretty close to 310, so selection D should be your answer.