Chapter 1.1, Problem 56E

Acquisition of Language The percentage $p\left(t\right)$ ofchildren who can speak in sentences of five or more words by the age of t months can be approximated by the equation¹⁵

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

a. Give a technology formula for p.

b. Graph p for $30\le t\le 45$ and $0\le p\le 100$.

c. Create a table of values of p for $t=30,31,\dots ,40$

(rounding answers to one decimal place).

d. What percentage of children can speak in sentences of five or more words by the age of 36 months?

e. By what age are 75% or more children speaking in sentences of five or more words?