Question

Please help! i dont understand this.

Answer 1

Answer:

Half life period = 43.11 days

Step-by-step explanation:

A sample substance has been taken for the use of drug research.

Weight of the substance taken = 0.25 gram

We have to use the formula of exponential decay to find the half life period of the substance.

Formula for the decay is $A_{t}=A_{0}e^{-kt}$

Where $A_{0}$ is the weight of the substance taken initially

$A_{t}$ is the quantity remained after t time

and t = time

Now we have to find the half life life period

$A_{t}$ = $\frac{0.25}{2}=.0125$

and $A_{0}=25$

By putting these values in the formula

0.125 = 25$e^{-0.1229t}$

$e^{-0.1229t}$ = $\frac{0.125}{25}$

$e^{-0.1229t}$ = 0.005

Now we take natural log on both the sides of the equation

$ln(e^{-0.1229t})=ln(.005)$

-0.1229t(lne) = -5.2983

0.1229t = 5.2983

t = $\frac{5.2983}{0.1229}=43.11 days$≈ 43.10 days

Therefore, half life period of the substance is 43.10 days

Answer 2

instead of using 0.41No you use 0.5No. rearranging the same way gives you t=(ln0.5)/(-k)=5.5 to the nearest 10th