Brain weight $ B $ as a function of body weight $ W $ in fish has been modeled by the power function $ B = 0.007W^{2/3}, $ where $ B $ and $ W $ are measured in grams. A model for body weight as a function of body length $ L $ (measured in centimeters) is $ W = 0. 12L^{2.53}. $ If, over 10 million years, the average length of a certain species of fish evolved from $ 15 cm $ to $ 20 cm $ at a constant rate, how fast was this species' brain growing when the average length was $ 18 cm? $

Two sides of a triangle have lengths $ 12 m $ and $ 15 m. $ The angle between them is increasing at a rate of $ 2^o/min. $ How fast is the length of the third side increasing when the angle between the side of fixed length is $ 60^o? $

Two carts, $ A $ and $ B, $ are connected by a rope $ 39 ft $ long that passes over a pulley $ P $ (see the figure). The point $ Q $ is on the floor $ 12 ft $ directly beneath $ P $ and between the carts. Cart $ A $ is being pulled away from $ Q $ at a speed of $ 2 ft/s. $ How fast is cart $ B $ moving toward $ Q $ at the instant when cart $ A $ is $ 5 ft $ from $ Q? $

A television camera is positioned $ 4000 ft $ from the base of a rocket launching pad. The angle of elevation of the camera has to change at the correct rate in order to keep the rocket in sight. Also, the mechanism for focusing the camera has to take into account the increasing distance from the camera to the speed is $ 600 ft/s $ when it has risen $ 3000 ft. $
(a) How fast is the distance from the television camera to the rocket changing at that moment?
(b) If the television camera is always kept aimed at the rocket, how fast is the camera's angle of elevation changing at that same moment?

A lighthouse is located on a small island $ 3 km $ away from the nearest point $ P $ on a straight shoreline and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from $ P? $