Chapter 4.3, Problem 55E

African Wild Dog The African wild dog is currently one of the most endangered carnivores in the world. After years of attempts to rescue the dog from extinction, scientists have collected a lot of data on the habits of this nomadic creature. The collected data show the following mathematical relationship between the weight and the length of the dog:

$L\left(w\right)=2.472w^{2.571},$

Where $w$ (in kg) is the weight and $L\left(w\right)$ (in mm) is the length of the mammal. Source: Journal of Mammalogy. Suppose that the weight of a particular wild dog can be estimated by

$w\left(t\right)=0.265+0.21t,$

Where $w\left(t\right)$ is the weight (in kg) and $t$ is the age, in weeks, of an African wild dog that is less than one year old. How fast is the length of a 25-week-old African wild dog changing?