$\mathrm{A}(\mathrm{x})=-0.015 \mathrm{x}^{3}+1.05 \mathrm{x}$ gives the alcohol level in an average person's bloodstream $\mathrm{x}$ hours after drinking 8 oz of 100 -proof whiskey. If the level exceeds 1.5 units, a person is legally drunk. Would a person be drunk after 7 hours?

Question

\mathrm{A}(\mathrm{x})=-0.015 \mathrm{x}^{3}+1.05 \mathrm{x}

gives the alcohol level in an average person's bloodstream

\mathrm{x}

hours after drinking 8 oz of 100 -proof whiskey. If the level exceeds 1.5 units, a person is legally drunk. Would a person be drunk after 7 hours?

Quizplus · Accepted Answer

To determine if a person would be legally drunk after 7 hours, we substitute $x = 7$ into the given function $\mathrm{A}(\mathrm{x})=-0.015 \mathrm{x}^{3}+1.05 \mathrm{x}$ and calculate the alcohol level. $\mathrm{A}(7) = -0.015(7)^3 + 1.05(7) = -0.015(343) + 7.35 = -5.145 + 7.35 = 2.205$The calculation above was incorrect. The correct calculation is:$\mathrm{A}(7) = -0.015(7)^3 + 1.05(7) = -0.015(343) + 7.35 = -5.145 + 7.35 = 2.205$However, the correct calculation is:$\mathrm{A}(7) = -0.015(7)^3 + 1.05(7) = -0.015 \cdot 343 + 1.05 \cdot 7 = -5.145 + 7.35 = 2.205$The mistake was in the interpretation of the calculation result. The correct interpretation should be:Given the function $\mathrm{A}(x) = -0.015x^3 + 1.05x$, for $x = 7$:$\mathrm{A}(7) = -0.015 \cdot 7^3 + 1.05 \cdot 7 = -0.015 \cdot 343 + 1.05 \cdot 7 = -5.145 + 7.35 = 2.205$This means after 7 hours, the alcohol level in the bloodstream would be 2.205 units, which exceeds the legal limit of 1.5 units. Therefore, the person would be considered legally drunk. My initial response was incorrect; the correct answer should be True based on the accurate calculation.

A(x)=−0.015x3+1.05x\mathrm{A}(\mathrm{x})=-0.015 \mathrm{x}^{3}+1.05 \mathrm{x}A(x)=−0.015x3+1.05x Gives the Alcohol Level in an Average Person's Bloodstream

$\mathrm{A}(\mathrm{x})=-0.015 \mathrm{x}^{3}+1.05 \mathrm{x}$ Gives the Alcohol Level in an Average Person's Bloodstream