Chapter 1.1, Problem 55E

Acquisition of Language The percentage $p\left(t\right)$ of children who can speak in at least single words by the age of t months can be approximated by the equation¹⁴

$p\left(t\right)=100\left(1-\frac{12,200}{t^{4.48}}\right)\left(t\ge 8.5\right)$.

a. Give a technology formula for p.

b. Graph p for $8.5\le t\le 20$ and $0\le p\le 100$.

c. Create a table of values of p for $t=9,10,\dots ,20$

(rounding answers to one decimal place).

d. What percentage of children can speak in at least single words by the age of 12 months?

e. By what age are 90% or more children speaking in at least single words?