another math question.. exponential decay.?

Question

the radioactive substance neptunium-139 decays to 73.6% of its original amount after 24 hours. What is the half life of neptunium-139?

Answer 1

N(t) = No * .5^(t/h)
N(24) = .736*No = No*.5^(24/h)
.736 = .5^(24/h)
convert to base e and take natural log of both sides
.736 = e^(ln(.5) * 24/h)
ln(.736) = ln(.5) * 24/h
h = ln(.5)*24/ln(.736)
or about 54.27134373 hours

Answer 2

The general equation is:
final amount = (initial amount)(1/2)^ (t/h) where h = length of halflife.

so you have 73.6 = 100 (1/2)^(24/h)

Divide both sides by 100: 0.736 = (1/2)^(24/h)

Take log of both sides making the exponent become a factor:

log (0.736) = (24/h) log (1/2)

Divide both sides by log (1/2) then cross multiply to solve for h

You know it's more than 24 hours because after 24 hours, more than half still remained

Answer 3

use hardship-unfastened develop equation of: x = Ao(a million + fee) ^time for decay - purely subtract distinction in values (ex. forty grams to 20 grams = 20 grams for fee) a million) 4000 = 4 hundred(a million + ok or r comparable element)^10 - sparkling up for ok 2) 20 = forty (a million + a million/2 or .050)^5/6 - comparable theory for develop and rot purely use a million/2 for fee cuz you like 0.5 existence - it is like that carbon relationship crap - to not undesirable. - wish this helped - probly not yet howdy, those issues is all muddle and puzzling, not confusing tho - hardship-unfastened arithmetic

Answer 4

16.304 hours

(not sure how many sig figs yur lookin for, so i gave you to the thousandth)