The following data defines the sea-level concentration of dissolved oxygen for fresh water as a function of temperature: T°C 8 16 24 32 40 o, mg/L I 14.621 11.843 9.870 8.418 6.413 Estimate o(27) using Newton's interpolating polynomial. Note that the exact result is 7.986 mg/L.

(b) What is an approximate value for e ?

Kleiber's Law states that the metabolic needs (such as calorie requirements) of a mammal are proportional to its body weight raised to the 0.75 power.¹ Surprisingly, the daily diets of mammals conform to this relation well. Assuming Kleiber's Law holds, answer the following questions. (a) Write a formula for C, daily calorie consumption, as a function of body weight, W. NOTE: Use k for the constant of proportionality. C(W) = (b) If a human weighing 150 pounds needs to consume 1800 calories a day, estimate the daily calorie requirement of a horse weighing 740 lbs and of a rabbit weighing 11 lbs. NOTE: Round your answers to the nearest calorie. Daily calorie requirement of a horse = Daily calorie requirement of a rabbit = calories Choose one calories (c) On a per-pound basis, which animal requires more calories: a mouse or an elephant? ¹S. Strogatz. "Math and the City." The New York Times. May 20, 2009. Kleiber originally

the sales revenue of a new mobile phone model is found to follow an AR(1) process, as shown below. what is the 3-lag AČF value? Xt =0.7*xt-1+Wt 0.700 .0.343 0.490 0.240

A tank is discharging water through an orifice at a depth x (m) below the surface of water whose area A (m²). The following are the values of the (corresponding values of (A) w.r.t (x : x (m) 1.5 1.65 1.8 1.95 2.10 225 24 255 27 2.85 3 A (m) 125 139 1.52 1.65 181 1.96 212 229 246 2.65 2.83 :Using the following formula 3.0 A dx T = 1.5 Calculate (T) for the level of water to drop from 1.5 m to 3 m by .Simpson's 1/3 rule

Given that f(-9.8) = 5.5 and f(-9.7) = 0.1, approximate f'(-9.8). f'(-9.8) 2

(c) Find a such that the equation P=100(1.23)′ can be written as P = 100eat. Give your answer correct to two decimal places.