Question

Explain how to write a composite function to find the area of the region at time t.

Answer 1

Answer:

$The composite function is:a(r(t)) = π (0.5 + 2t)²After simplification it becomes:a(r(t)) = π (0.25 + 2t + 4t²)Step-by-step explanation:Here is the complete function:a circular oil spill continues to increase in size. the radius of the oil spill, in miles, is given by the function r(t) = 0.5 + 2t, where t is the time in hours. the area of the circular region is given by the function a(r) = πr², where r is the radius of the circle at time t. Explain how to write a composite function to find the area of the region at time t.Solution:The composite function is written by applying one function to another. The requirement of this question is to write a composite function to find are of region at time t.Leta(r) = πr²is function 1andr(t) = 0.5 + 2tis function 2ThenThis means that function r(t) should be applied to a(r) and it should be inside function a(r)Then composite function becomes:a(r(t))Now put the value of r(t) = 0.5 + 2t into a(r) = πr²a(r(t)) = π (0.5 + 2t)²So this is the composite function to find area of the region at time tSimplifying this equation we get:a(r(t)) = π (0.5 + 2t)² = π (0.5 + 2t) (0.5 + 2t) = π [(0.5 * 0.5)+ (0.5 * 2t) + (2t * 0.5) + (2t *2t)] = π (0.25 + 1t + 1t + 4t²) = π ( 0.25 + t + t + 4t²) = π (0.25 + 2t + 4t²)a(r(t)) = π (0.25 + 2t + 4t²)$

Step-by-step explanation:

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