The force of interest, 8(t), is a function of time and at any time t, measured in years, is given by the formula: 0.06, 0.100.01 8(t) = 0≤ t ≤ 4; 4 < t <7; 0.01 0.04 7

A certain population has a yearly growth of 2.3%. If there are initially 3 million people, find a formula to express the population P, in millions of people; as a function of time t in years.

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