Question: How to use log transfromation in Maple?

Duarte and Agustí (1998) investigatedthe CO2 balance o f  aquati  c ecosystems. They related thecommunity respiration rates (R) to the gross primary production rates (P) of aquatic ecosystems. (Both quantities were measured in the same units.) They made the following statement:

Our results  confirm the generality of earlier reports that the relation between community respiration rate andgross production is not linear. Community respirationis scaled as the approximate two-thirds power of grossproduction.

(a) Suppose that you obtained data on the gross production and respiration rates of a number of freshwater lakes. How would you display your data graphically to quickly convince an audience that the exponent b in the power equation relating Rand P is indeed approximately 2/3? (Hint: Use an appropriate log transformation in Maple)

(c) The r atio R/P for an ecosystem is important in assessing the global CO2 budget. If respiration exceeds production (i.e., R >P), then the ecosystem acts as a carbon dioxide source, whereas if production exceeds respiration (i.e., P > R), then the ecosystema cts as a carbon dioxide sink. Assume now that the exponent inthe power equation relating R and P is 2/3. Show that the ratio R/P, as a function of P, is continuous for P > 0. Furthermore,show that
           lim R/P =∞
            P→0+

and
            lim R/P= 0
            P→∞


How to use Maple to sketch the graph of the ratio R/P as  afunction of P for P > 0. (Experiment with the graphing calculatorto see how the value of a affects the graph.)