Answer:
[tex]a(t) =n(0.25t^2)[/tex]
Step-by-step explanation:
Given
[tex]r(t) = 0.5t[/tex]
[tex]a(r) = nr^2[/tex]
Required
Determine the area in terms of time
From the question, we have:
[tex]r(t) = 0.5t[/tex] -> radius per time
and
[tex]a(r) = nr^2[/tex] --> area from radius
The interpretation of the question is to find the composite function: a(t)
If [tex]a(r) = nr^2[/tex], and [tex]r(t) = 0.5t[/tex], the
Substitute 0.5t for r
[tex]a(t) =n(0.5t)^2[/tex]
[tex]a(t) =n*0.25t^2[/tex]
[tex]a(t) =n(0.25t^2)[/tex]
