A radioactive compound with mass 180 grams decays at a rate of 4% per hour. Which equation represents how many grams of the compound will remain after 8 hours? C=180(0.96)^(8) C=180(1-0.04)(1-0.04)(1-0.04) C=180(1+0.04)^(8) C=180(1-0.4)^(8)

Question

A radioactive compound with mass 180 grams decays at a rate of  4% per hour. Which equation represents how many grams of the compound will remain after 8 hours?  C=180(0.96)^(8)  C=180(1-0.04)(1-0.04)(1-0.04)  C=180(1+0.04)^(8)  C=180(1-0.4)^(8)

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Understand the problem: Understand the problem. We need to find the equation that correctly represents the decay of a radioactive compound that starts with a mass of 180 grams and decays at a rate of 4% per hour over a period of 8 hours.Identify the correct decay formula: Identify the correct decay formula. The general formula for exponential decay is given by C = C0 * (1 - r)^t, where C0 is the initial amount, r is the decay rate per unit time, and t is the time.Substitute values into formula: Substitute the given values into the decay formula. C0 = 180 grams (initial amount), r = 4% per hour (decay rate), and t = 8 hours (time). Convert the percentage decay rate to a decimal: 4% = 0.04.Write equation with values: Write the equation using the values from Step 3. C = 180 * (1 - 0.04)^8Check for matching equation: Check the given options to see which one matches the equation from Step 4. The correct equation is C = 180 * (1 - 0.04)^8, which simplifies to C = 180 * (0.96)^8.Verify other options: Verify that none of the other options match the correct equation. Option B: C = 180 * (1 - 0.04)(1 - 0.04)(1 - 0.04) is incorrect because it only accounts for three hours of decay, not eight. Option C: C = 180 * (1 + 0.04)^8 is incorrect because it suggests growth, not decay. Option D: C = 180 * (1 - 0.4)^8 is incorrect because the decay rate is 4%, not 40%.

A radioactive compound with mass $180$ grams decays at a rate of $4 \%$ per hour. Which equation represents how many grams of the compound will remain after $8$ hours? $\newline$ $C=180(0.96)^{8}$ $\newline$ $C=180(1-0.04)(1-0.04)(1-0.04)$ $\newline$ $C=180(1+0.04)^{8}$ $\newline$ $C=180(1-0.4)^{8}$

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