need help pls How long will it take a sample of radioactive

need help pls

How long will it take a sample of radioactive substance to decay to half of its original amount if it decays according to the function A(t) - 750 E^-0.144t, Where t is the time in years? Round to the nearest hundredth year. 108.00 yr 50.79 yr 45.97 yr 4.81 yr

Solution

the given expression is A(t) = 750 e^-0.144t

the initial amount is at t =0

A(0) = 750 e^0

=750

now we have to find the time to take 750/2

750/2 = 750 e^-0.144t

1/2 = e^-0.144t

apply ln to each side

ln(1/2) = ln(e^-0.144t)

-0.693 = -0.144t

0.144t =0.693

t = 0.693/0.144

t = 4.81 years

so Option D) is correct