Respuesta :
Answer:
Write the composition A compose r: A(r(tt)).
The function r(t) is the inside function or input in function A(r)
Substitute 0.5 +2t into the area formula in place of r: A(r(tt)) = pi(0.5+2t)^2
Step-by-step explanation:
A function assigns the values. The composite function to find the area of the region at time t is A(r(t))=(4t² + 2t + 0.25)π.
What is a Function?
A function assigns the value of each element of one set to the other specific element of another set.
Given that the radius of the oil spill, in miles, is given by the function r(t)=0.5+2t, where t is the time in hours.
Also, The area of the circular region is given by the function A(r)=πr², where r is the radius of the circle at time t.
Therefore, a composite function to find the area of the region at time t can be written as,
A(r(t)) = π r²
= π (0.5 + 2t)²
= π (0.5² + 4t² + 2(0.5)(2t))
= π (0.25 + 4t² + 2t)
= (4t² + 2t + 0.25)π
Hence, the composite function to find the area of the region at time t is A(r(t))=(4t² + 2t + 0.25)π.
Learn more about Function:
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