Answer:
[tex]A(t) = \pi (0.5 + 2t)^2[/tex]
Step-by-step explanation:
Given
[tex]r(t) = 0.5 + 2t[/tex]
[tex]A(r) = \pi r^2[/tex]
Required
Determine composite function to find A in terms of t
The interpretation of this question is to determine A(t) and this is solved as follows:
Because:
[tex]r(t) = 0.5 + 2t[/tex]
And we want to eliminate r in [tex]A(r) = \pi r^2[/tex]
We have to substitute 0.5 + 2t for r in [tex]A(r) = \pi r^2[/tex]
[tex]A(r) = \pi r^2[/tex] becomes
[tex]A(t) = \pi (0.5 + 2t)^2[/tex]
The solution can be solved further, but it is best left in this form:
[tex]A(t) = \pi (0.5 + 2t)^2[/tex]
