Chapter 10.4, Problem 2E

The demand for watches is given by p = 7000 − 2q dollars,and the supply of watches is given by p = 0.01q^2+ 2q + 1000 dollars,where q is the number of watches demanded and supplied when the price perwatch is p dollars. Based on the information provided, calculate the equilibriumquantity and the equilibrium price for watches.

The population oftan endangered species of rhinos in 2006 was estimated to be 100,507 rhinos. By 2012, the number of rhinos had grown to 245,957. (a) Assuming the population grows linearly, find the linear model, y = mx + b, representing the population x years since 2000. y = Number x + Number (round m and b to 3 decimal places) (b) Using the linear model from part (a), estimate the population in 2025. Number (round to the nearest whole number)

As with discrete-time dynamical systems, equilibria can act strange when the slope of the rate-of-change function is exactly equal to the critical value of zero. Graph a rate-of-change function that has a slope of 0 at the equilibrium but the equilibrium is stable. What is the sign of the second derivative at the equilibrium? What is the sign of the third derivative at the equilibrium?