Final answer:
To linearize the data for volume and time, if a power law or exponential growth is expected, the logarithm of both quantities should be taken. Therefore, the correct choice is D) ln(Seconds), ln(cm³).
Step-by-step explanation:
The question asks about linearizing the relationship between volume and time. If a relationship between two variables is not linear but can be described by a certain power law or exponential growth, we may use the logarithm to linearize the data. One general approach is that if you suspect a power law relationship of the form V = ktn, where V is volume and t is time, you would take the logarithm of both sides to yield log(V) = log(k) + n*log(t), resulting in a linear equation y = mx + b when using log(V) and log(t).
If an exponential relationship is suspected, such as V = k*et, where e is the base of the natural logarithm, you would use the natural logarithm to linearize the data. You would take the natural logarithm of both sides to obtain ln(V) = ln(k) + t, which is also a linear equation. Therefore, if we're linearizing the data for the variables volume and time, and suspect either a power law or exponential growth, the proper transformation would involve taking the logarithm of both quantities.
The correct answer would thus be: D) ln(Seconds), ln(cm³).