A radioactive compound with mass 280 grams decays at a rate of 18.3% per hour. Which equation represents how many grams of the compound will remain after 2 hours? C=280(1.183)^(2) C=280(1-0.183)(1-0.183) C=280(1+0.183)^(2) C=280(1-0.183)(1-0.183)(1-0.183)(1-0.183)

Question

A radioactive compound with mass 280 grams decays at a rate of  18.3% per hour. Which equation represents how many grams of the compound will remain after 2 hours?  C=280(1.183)^(2)  C=280(1-0.183)(1-0.183)  C=280(1+0.183)^(2)  C=280(1-0.183)(1-0.183)(1-0.183)(1-0.183)

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Decay Factor Calculation: Understand the decay rate and convert it to a decay factor. The decay rate is given as 18.3% per hour, which means that each hour, the compound loses 18.3% of its mass. To find the decay factor, we subtract the decay rate from 1 (since 1 represents the whole mass). Decay factor = 1 - decay rate Decay factor = 1 - 0.183 Decay factor = 0.817Exponential Decay Equation Formulation: Write the exponential decay equation using the decay factor. The general form of the exponential decay equation is C = initial_mass * (decay_factor)^time. Here, the initial mass (C0) is 280 grams, the decay factor we found in Step 1 is 0.817, and the time (t) is 2 hours. C = 280 * (0.817)^2Options Comparison: Check the given options to see which one matches the equation we derived. Option A: C=280(1.183)^(2) - This option is incorrect because it suggests an increase by 18.3% instead of a decrease. Option B: C=280(1-0.183)(1-0.183) - This option is correct because it represents the mass after two hours, taking into account the decay rate twice. Option C: C=280(1+0.183)^(2) - This option is incorrect because it suggests an increase by 18.3% instead of a decrease. Option D: C=280(1-0.183)(1-0.183)(1-0.183)(1-0.183) - This option is incorrect because it suggests the decay happens over four hours instead of two.

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