Question

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? 5.7 mg 2.0 mg 2.5 mg 7.1 mg

Explanation:

Step1: Identify values

$A = 10$ mg, $h = 8$ days, $t = 16$ days

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

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

Step4: Calculate power

$(\frac{1}{2})^2=\frac{1}{4}$, so $P(16)=10\times\frac{1}{4}$

Step5: Calculate final amount

$10\times\frac{1}{4} = 2.5$ mg

Answer:

2.5 mg