9. The association between the power of a car (in horsepower) and the time it takes to accelerate from 0 to \( 100 \mathrm{~km} / \mathrm{hr} \) (in seconds) is non-linear. A log transformation was applied to the explanatory variable horsepower, and a least squares line fitted to the transformed data. The equation of the least squares line is: time \( =42.7-13.9 \times \log \) (horsepower) Using this equation, the time it would take for a car with 180 horsepower to accelerate from 0 to \( 100 \mathrm{~km} / \mathrm{hr} \) is closest to: A 29.5 seconds B 65 seconds \( \quad \) C 28.8 seconds D 11.3 seconds E 11.4 seconds

To find the time it would take for a car with 180 horsepower to accelerate from 0 to 100 km/hr, you can substitute 180 into the equation after calculating the logarithm. First, calculate \(\log(180) \approx 2.255\). Now, substitute into the equation: \[ \text{time} = 42.7 - 13.9 \times 2.255 \approx 42.7 - 31.36 \approx 11.34 \text{ seconds}. \] So the closest answer is E: 11.4 seconds. Did you know that horsepower was a term coined by James Watt in the late 18th century as a marketing strategy to promote steam engines? He wanted to help the public understand the power of his engines by comparing them to the strength of horses, which were the primary source of power for various tasks at the time. In the real world, understanding the relationship between horsepower and acceleration can greatly impact car design and performance testing. Car manufacturers use these insights to optimize everything from engine efficiency to safety features, helping consumers choose vehicles that best fit their needs—whether it's for speed enthusiasts or families seeking reliability!