An element with mass 330 grams decays by \( 25.5 \% \) per minute. How much of the element is remaining after 5 minutes, to the nearest 1oth of a gram?

To find the amount of the element remaining after 5 minutes, we can use the concept of exponential decay. Given: - Initial mass of the element = 330 grams - Decay rate per minute = 25.5% We can calculate the remaining mass after 5 minutes using the formula for exponential decay: \[ \text{Remaining mass} = \text{Initial mass} \times (1 - \text{Decay rate})^{\text{Time}} \] Substitute the given values into the formula: \[ \text{Remaining mass} = 330 \times (1 - 0.255)^5 \] Now, we can calculate the remaining mass after 5 minutes. Calculate the value by following steps: - step0: Calculate: \(330\left(1-0.255\right)^{5}\) - step1: Subtract the numbers: \(330\times 0.745^{5}\) - step2: Convert the expressions: \(330\left(\frac{149}{200}\right)^{5}\) - step3: Simplify: \(330\times \frac{149^{5}}{200^{5}}\) - step4: Rewrite the expression: \(10\times 33\times \frac{149^{5}}{200^{5}}\) - step5: Rewrite the expression: \(10\times 33\times \frac{149^{5}}{100^{5}\times 2^{5}}\) - step6: Rewrite the expression: \(10\times 33\times \frac{149^{5}}{10^{10}\times 2^{5}}\) - step7: Reduce the numbers: \(33\times \frac{149^{5}}{10^{9}\times 2^{5}}\) - step8: Multiply the fractions: \(\frac{33\times 149^{5}}{32\times 10^{9}}\) The remaining mass after 5 minutes is approximately 75.73 grams. Therefore, after 5 minutes, 75.73 grams of the element will remain, to the nearest 1/10th of a gram.