QuestionThe half-life of a drug in the bloodstream is 22 hours. What fraction of the original drug dose remains in 48 hours? in 72 hours?
What fraction of the original drug dose remains in 48 hours? $\square$ (Do not round until the final answer. Then round to the nearest hundredth as needed.) What fraction of the original drug dose remains in 72 hours? $\square$ (Do not round until the final answer. Then round to the nearest hundredth as needed.)

Studdy Solution
Calculate the fraction remaining after 72 hours.
Substitute $t = 72$ into the formula:
$$N(72) = N_0 \left(\frac{1}{2}\right)^{\frac{72}{22}}$$
Calculate the exponent:
$$\frac{72}{22} \approx 3.2727$$
Now calculate the fraction:
$$N(72) = N_0 \left(\frac{1}{2}\right)^{3.2727}$$
$$N(72) = N_0 \times 0.099$$
The fraction of the original dose remaining after 72 hours is approximately:
$$\boxed{0.10}$$