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A radioactive compound with mass 330 grams decays at a rate of
21% per hour. Which equation represents how many grams of the compound will remain after 4 hours?

C=330(1-0.21)

C=330(1.21)^(4)

C=330(1+0.21)^(4)

C=330(1-0.21)(1-0.21)(1-0.21)(1-0.21)

A radioactive compound with mass $330$ grams decays at a rate of $21 \%$ per hour. Which equation represents how many grams of the compound will remain after $4$ hours? $\newline$ $C=330(1-0.21)$ $\newline$ $C=330(1.21)^{4}$ $\newline$ $C=330(1+0.21)^{4}$ $\newline$ $C=330(1-0.21)(1-0.21)(1-0.21)(1-0.21)$

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Write exponential functions: word problems

Full solution

Q. A radioactive compound with mass

330

grams decays at a rate of

21 \%

per hour. Which equation represents how many grams of the compound will remain after

4

hours?

\newline

C=330(1-0.21)

\newline

C=330(1.21)^{4}

\newline

C=330(1+0.21)^{4}

\newline

C=330(1-0.21)(1-0.21)(1-0.21)(1-0.21)

Question Prompt: The question prompt is: ＂Which equation represents how many grams of the compound will remain after $4$ hours?＂
Decay Process: First, we need to understand the decay process. The compound decays at a rate of $21\%$ per hour, which means that each hour, only $79\%$ ( $100\% - 21\%$ ) of the compound remains.
Exponential Equation: To represent this decay as an exponential equation, we use the formula $C = \text{initial\_amount} \times (\text{decay\_factor})^{\text{time}}$ , where the decay factor is $1$ minus the decay rate (expressed as a decimal).
Convert Decay Rate: Convert the decay rate of $21\%$ to a decimal by dividing by $100$ . This gives us $0.21$ .
Find Decay Factor: Subtract the decay rate in decimal form from $1$ to find the decay factor. This gives us $1 - 0.21 = 0.79$ .
Write Decay Equation: Now we can write the exponential decay equation using the initial amount of $330$ grams and the decay factor of $0.79$ . The time is represented by the variable $t$ , which in this case is $4$ hours. So the equation is $C = 330 \times (0.79)^t$ .
Substitute Time: Substitute $4$ for $t$ in the equation to find the amount of compound remaining after $4$ hours. This gives us $C = 330 \times (0.79)^4$ .

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