Question

7. A particular compound decays according to the equation y = ae-0.0736t, where tis in days. Find the

half-life of this compound.
a. about 9.1 days b. about 9.4 days
c. about 6.8 days d. about 7.4 days

Answer 1

b. about 9.4 days

Explanation:

Amount of the compound:

The amount of the compound after t days is given by the following equation:

`y(t) = ae^(-0.0736t)`

The initial amount is:

`y(0) = a`

Half-life:

t for which
`y(t) = 0.5a`. So

`y(t) = ae^(-0.0736t)`

`0.5a = ae^(-0.0736t)`

`e^(-0.0736t) = 0.5`

`\ln{e^(-0.0736t)} = ln(0.5)`

`-0.0736t = ln(0.5)`

`t = -(ln(0.5))/(0.0736)`

`t = 9.42`

So about 9.4 days, and the answer is given by option b.