5. an isotope of sodium, na - 24 has a half - life of 15 h. find the amount remaining from a 4 g sample…

5.

Explanation:

Step1: Convert time to hours

There are 24 hours in a day. So 3 days is $3\times24 = 72$ hours.

Step2: Calculate the number of half - lives

The number of half - lives $n=\frac{t}{T_{1/2}}$, where $t$ is the total time and $T_{1/2}$ is the half - life. Given $T_{1/2}=15$ h and $t = 72$ h, so $n=\frac{72}{15}=4.8$.

Step3: Use the radioactive decay formula

The formula for radioactive decay is $N = N_0\times(\frac{1}{2})^n$, where $N_0$ is the initial amount and $N$ is the final amount. Here $N_0 = 4$ g and $n = 4.8$. So $N=4\times(\frac{1}{2})^{4.8}$. We know that $(\frac{1}{2})^{4.8}=2^{- 4.8}$. Using a calculator, $2^{-4.8}\approx0.037$. Then $N = 4\times0.037=0.148$ g.

Answer:

$0.148$ g

6.

Explanation:

Step1: Use the depreciation formula

The formula for depreciation is $A = P(1 - r)^t$, where $A$ is the final value, $P$ is the initial value, $r$ is the rate of depreciation per year, and $t$ is the number of years. We are given that $A = 4200$, $r=0.15$, and $t = 5$. We need to solve for $P$.

Step2: Rearrange the formula to solve for $P$

From $A = P(1 - r)^t$, we can get $P=\frac{A}{(1 - r)^t}$. Substitute the given values: $(1 - r)=1 - 0.15 = 0.85$ and $t = 5$. So $(1 - r)^t=(0.85)^5$. Using a calculator, $(0.85)^5=0.85\times0.85\times0.85\times0.85\times0.85\approx0.4437$. Then $P=\frac{4200}{0.4437}\approx9466$.

Answer:

$$9466$