The percentage $p ( t )$ of children who are able to speak in at least single words by the age of t months can be approximated by the equation.
$p ( t ) = 100 \left( 1 - \frac { 12,188 } { t ^ { 4.42 } } \right)$
By what age are 70% of children speaking in at least single words Round your answer to the nearest month.
A)16
B) 7
C) 11
D) 5
E) 8

Question

The percentage $p ( t )$ of children who are able to speak in at least single words by the age of t months can be approximated by the equation.  
 $p ( t ) = 100 \left( 1 - \frac { 12,188 } { t ^ { 4.42 } } \right)$  
By what age are 70% of children speaking in at least single words  Round your answer to the nearest month.
A)16
B) 7
C) 11
D) 5
E) 8

Quizplus · Accepted Answer

To find the age $t$ at which 70% of children are speaking in at least single words, we set $p(t) = 70$ and solve for $t$:$$70 = 100 \left( 1 - \frac { 12,188 } { t ^ { 4.42 } } \right)$$Solving this equation involves isolating $t$, which requires algebraic manipulation:$$0.7 = 1 - \frac { 12,188 } { t ^ { 4.42 } }$$$$\frac { 12,188 } { t ^ { 4.42 } } = 0.3$$$$t ^ { 4.42 } = \frac { 12,188 } { 0.3 }$$$$t ^ { 4.42 } = 40,626.67$$$$t = \sqrt[4.42]{40,626.67}$$Solving this gives a value of $t$ that is approximately 11 months, rounding to the nearest month.

The Percentage p(t)p ( t )p(t) Of Children Who Are Able to Speak in at Least

The Percentage $p ( t )$ Of Children Who Are Able to Speak in at Least