smith put some money in a saving certificate which earns 8% a year. the yearly interest in $600. how much did smith invest?

1 answer:

6 0

$~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill&\$600\\ P=\textit{original amount deposited}\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &1 \end{cases} \\\\\\ 600=P(0.08)1\implies \cfrac{600}{0.08}=P\implies 7500=P$

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Between the years of 1947 and 1956, earthenware jars containing what are known as the Dead Sea Scrolls were found in caves along

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Answer:

They are right, the time calculated using the exponential decay equation is 1948.6 years.

Step-by-step explanation:

The time can be calculated using the exponential decay equation:

$N_{(t)} = N_{0}e^{-\lambda t}$ (1)

<u>Where</u>:

N(t): is the quantity of C-14 at time t

N₀: is the initial quantity of C-14

λ: is the decay constant

The decay constant is:

$\lambda = \frac{ln(2)}{t_{1/2}}$ (2)

By entering equation (2) into (1) and solving for t, we have:

$t = \frac{t_{1/2}*ln(N_{t}/N_{0})}{ln(2)} = \frac{5730*ln(0.79)}{ln(2)} = 1948.6 y$

Therefore, the time of the scrolls estimated by the archeologists is right, since the time calculated using the exponential decay equation is 1948.6 years.

I hope it helps you!

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