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- Plant Growth Researchers have found that the probability P that a plant will grow to radius R can be described by the differential equation dPdR=4DRP2 where D is the density of the plants in an area. Source: Ecology. Given the initial condition P(0)=1, find a formula for P in term of R.Use the total differential to approximate each quantity. Then use a calculator to approximate the quantity, and give the absolute value of the differences in the two results to 4decimal places. (2.9320.942)13Use the differential to approximate each quantity. Then use a calculator to approximate the quantity, and give the absolute value of the difference the two results to 4decimal places. e0.002
- Multivariable Calculus Total Differentials and Approximations LIFE SCIENCE APPLICATIONS Heat Loss In Exercise 50 of Section 2 of this chapter, we found that the rate of heat loss in watts in harbor seal pups could be approximated by H(m,T,A)=15.2m0.67(TA)10.23lnm10.74 Where m is the body mass of the pup in kg, and T and A are the body core temperature and ambient water temperature, respectively in C. Suppose m is 25kg, T is 36.0, and A is 12.0, Approximate the change in H if m changes to 26kg,T to 36.5 and A to 10.0.Multivariable Calculus Total Differentials and Approximations LIFE SCIENCE APPLICATIONS Blood Volume In Exercise 52 of Section 2 in this chapter, we found that the number of liters of blood pumped through the lungs in one minute is given by C=bav Suppose a=160,b=200 and v=125. Estimate the change in C if a becomes 145,b becomes 190, and v changes to 130.Multivariable Calculus Total Differentials and Approximations LIFE SCIENCE APPLICATIONS Horn Volume The volume of the horns from bighorn sheep was estimated by researchers using the equation V=h3(r21+r1r2+r22) where h is the length of a horn segment in centimeters and r1 and r2 are the radii of the two ends of the horn segment in centimeters. Source: Conservation Biology. a. Determine the volume of the segment of horn that is 40cm long with radii of 5cm and 3cm, respectively. b. Use the total differential to estimate the volume of the segment of horn if the horn segment from part a was actually 42cm long with radii of 5.1cm and 2.9cm, respectively. Compare this with the actual volume.