Question

in 2000, 50 grams of radium were stored. the half - life of radium is 1,620 years. how many grams of radium remains after 4860 years? 2.50 grams 12.5 grams 6.25 grams 25 grams question 14 1 pts a new car was purchased at a cost of $25,000. the car depreciates approximately 15% of its value each year. the car will be worth $4,921.86 in 10 years. false true

Explanation:

Step1: Calculate the number of half - lives

The formula for the number of half - lives \(n=\frac{t}{T}\), where \(t = 4860\) years (time elapsed) and \(T=1620\) years (half - life).
\(n=\frac{4860}{1620}=3\)

Step2: Use the radioactive decay formula

The formula for radioactive decay is \(N = N_0\times(\frac{1}{2})^n\), where \(N_0 = 50\) grams (initial amount) and \(n = 3\) (number of half - lives).
\(N=50\times(\frac{1}{2})^3\)
\(N = 50\times\frac{1}{8}\)
\(N=6.25\) grams

Step1: Use the compound - depreciation formula

The formula for compound depreciation is \(A=P(1 - r)^t\), where \(P=\$25000\) (initial value), \(r = 0.15\) (rate of depreciation), and \(t = 10\) (number of years).
\(A=25000\times(1 - 0.15)^{10}\)
\(A=25000\times(0.85)^{10}\)

Step2: Calculate \((0.85)^{10}\)

\((0.85)^{10}\approx0.1968744\)

Step3: Calculate the value of the car after 10 years

\(A=25000\times0.1968744=\$4921.86\)

Answer:

6.25 grams

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