Question 522·Hard·Algebra

The dashboard rule applies at each distance. Substitute the given display readings for $p(10)$ and $p(22)$, while keeping the actual percentages unknown:

Let $u_1$ stand for $B(10)$. Type $\frac45u_1-5\sim51$; the $\sim$ tells Desmos to find a value that fits the equation. Under PARAMETERS, it shows $u_1=70$. So the actual battery percentage at $10$ miles is $70$, not the displayed $51$.

Keep $u_1$ for $B(10)$, and let $v_1$ stand for $B(22)$. Add $\frac45v_1-5\sim35$. Desmos shows $v_1=50$ under PARAMETERS. So the second actual battery percentage is $50$.

The drone goes from $70$ to $50$ actual percent while traveling from $10$ to $22$ miles. Slope means output change divided by input change, so type $\frac{v_1-u_1}{22-10}$. Desmos shows about $-1.6667$; its fraction button gives $-\frac53$. That is the slope of $B$, not the slope of the dashboard graph.

Write the linear rule as $B(x)=mx+b$, where $b$ is the percentage at $x=0$, called the $y$-intercept. The converted point $(10,70)$ and slope $m=-\frac53$ give:

Subtract the slope term from both sides:

Type that expression in Desmos. It shows about $86.6667$; the fraction button gives $\frac{260}{3}$. So the drone’s actual battery percentage is $B(x)=-\frac53x+\frac{260}{3}$. Choice A.