Wind speed varies in the first twenty meters above the ground. For a particular day, let $f ( x ) = 9.8 \ln x + 3.3$ model the wind speed $x$ meters above the ground. At what height is the wind speed 9 meters per second? Round results to the nearest hundredth.
A) 1.79 m
B) 0.58 m
C) 0.49 m
D) 0.56 m

Question

Quizplus · Accepted Answer

To find the height at which the wind speed is 9 meters per second, set the equation $9.8 \ln x + 3.3 = 9$ and solve for $x$. Subtract 3.3 from both sides to get $9.8 \ln x = 5.7$. Divide both sides by 9.8 to get $\ln x = \frac{5.7}{9.8}$. Exponentiate both sides to solve for $x$, leading to $x = e^{\frac{5.7}{9.8}}$. Calculating this gives $x \approx 1.79$, which means the wind speed is 9 meters per second at approximately 1.79 meters above the ground.

Wind Speed Varies in the First Twenty Meters Above the Ground