the amount of a sample remaining after t days is given by the equation $p(t)=a(\frac{1}{2})^{\frac{t}{h}}$…

the amount of a sample remaining after t days is given by the equation $p(t)=a(\frac{1}{2})^{\frac{t}{h}}$, where a is the initial amount of the sample and h is the half - life, in days, of the substance. a scientist has a 10 - mg sample of a radioactive isotope. the isotope has a half - life of 8 days. after 16 days, how much of the radioactive isotope remains?\n2.0 mg\n2.5 mg\n5.7 mg\n7.1 mg

the amount of a sample remaining after t days is given by the equation $p(t)=a(\frac{1}{2})^{\frac{t}{h}}$, where a is the initial amount of the sample and h is the half - life, in days, of the substance. a scientist has a 10 - mg sample of a radioactive isotope. the isotope has a half - life of 8 days. after 16 days, how much of the radioactive isotope remains?\n2.0 mg\n2.5 mg\n5.7 mg\n7.1 mg

Answer

Explanation:

Step1: Identify values

$A = 10$ (initial amount), $h = 8$ (half - life), $t = 16$ (time).

Step2: Substitute into formula

$P(t)=A(\frac{1}{2})^{\frac{t}{h}}$, so $P(16)=10\times(\frac{1}{2})^{\frac{16}{8}}$.

Step3: Calculate exponent

$\frac{16}{8}=2$, then $P(16)=10\times(\frac{1}{2})^2$.

Step4: Calculate power

$(\frac{1}{2})^2=\frac{1}{4}$.

Step5: Calculate final amount

$P(16)=10\times\frac{1}{4}=2.5$.

Answer:

2.5 mg