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

Answer:

b. about 9.4 days

Step-by-step 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

$y(t) = ae^{-0.0736t}$

$0.5a = ae^{-0.0736t}$

$e^{-0.0736t} = 0.5$

$\ln{e^{-0.0736t}} = \ln{0.5}$

$-0.0736t = \ln{0.5}$

$t = -\frac{\ln{0.5}}{0.0736}$

$t = 9.42$

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