A circular oil spill continues to increase in size. 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. 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.
Explain how to write a composite function to find the area of the region at time t.
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Answer:
a circular oil spill continues to increase in size. 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. 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.
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Answer:
4πt² + 2πt + 0.25π
Step-by-step explanation:
We know the function for area in terms of radius and the function for radius in terms of time. Substituting the second into the first gives us the composite function required, i.e. A(r(t)).
A(r(t)) = A(0.5+2t) = π(0.5 + 2t)²
= π(4t²+ 2t + 0.25)
= 4πt² + 2πt + 0.25π
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