Question

a 40 gram sample of a substance that's used for drug research has a k-value of 0.1446. find the substance's half life in days

Answer 1

The applicable decay formula is:N = No*e^(-kt)WhereN = Mass left after time tNo = Original massk = constantt = half lifeUsing the values given,N/No = e^(-0.1446t) = 1/2ln (1/2) = -0.1446 t *ln e^1-0.6931 = -0.1446 tt = 0.6331/0.1446 = 4.79 daysTherefore, half-life is 4.8 days.

Answer 2

4.7935 days

Explanation:

The expression that describes exponential decay is the following:

N(t) = No *
`e^(-kt)`

Where N(t) is the mass of the substance after a period t of time.

No is the original amount of substance

k is the relative decay rate and t is the period of time elapsed.

The half life is the period of time after which the amount of substance has decreased by half.

We can issolate t in the expression, using the properties of logarithms:

`(N(t))/(No)`=
`e^(-kt)`

ln(
`(N(t))/(No)`) = -k*t

t = - ln(
`(N(t))/(No)`)/k = - ln(
`(1)/(2)`)/0.1446 = 4.7935 days.