The halflife of dubnium261 is 27 seconds If there are 36 gra

The half-life of dubnium-261 is 27 seconds. If there are 36 grams present initially, write a function that gives the amount remaining as a function of time.

Solution

half life of dubnium -261 = 27 seconds

initial amount = 36 grams

standard equation of exponential function is

P = Po e^kt

where , P = final amount

Po = initial amount

t = time

k = growth/decay constant

plugging the values in exponetial equation

18 = 36 e^k(27)

dividing equation by 36

1/2 = e^k(27)

taking ln on both sides

ln (1/2) = 27 k ln e

-.69314 = 27 k

k = -.0256

therefore, function would be

P = 36 e^(-.0256 t )