Chapter 3.3, Problem 100E

Acquisition of Language The percentage $q\left(t\right)$ ofchildren who can speak in sentences of five or more words by the age of t months can be approximated by the equation

$q\left(t\right)=100\left(1-\frac{5.27\times {10}^{17}}{t^{12}}\right)\left(t\ge 30\right).$

If p is the function referred to in the preceding exercise, Calculate ${\lim }_{x\to +\infty }\left[p\left(t\right)-q\left(t\right)\right],$ andinterpret the result. [HINT: See Example 4.]