Researchers have found a correlation between respiratory rate and body mass in the first three years of life. This correlation can be expressed by the function log R(w) = 1.85-0.48 log (w), where w is the body weight (in kilograms) and R(w) is the respiratory rate (in breaths per minute). a. Find R'(w) using implicit differentiation. b. Find R'(w) by first solving the equation for R(w). c. Discuss the two procedures. Is there a situation when you would want to use one method over another?

An invasive population of 40,000 Nutria is being hunted in a local swamp. The amount of Nutria hunted over time is given by the following equation 1,000,000/(t + 5)2 .  A. Find the derivative of the Nutria hunted over time. B. At what rate is the Nutria population decreasing after 15 years?

Find the derivative of the function. h(x) = log,(x2 + x) h'(x) =

When drugs are administered into the bloodstream, the amount of the drug present decreases continuously at a constant rate. The amount of a certain drug, Xanaz, in the bloodstream is modeled by the function, where is the initial dosage, and t is the time (in hours) after the initial dose was given. The following chart shows the relationship between the original dose and how much is sti in the system after so much time. Xanax (3mg) amount still in system after X hours 2.5 1.5 0.5 2 10 12 14 16 18 20 22 24 Number of hours after dose was taken After how many hours will there be approximately 1/2 of the original dose in the body? 3. 2. 1. Amount still in the system in mg's