Due to a lightning strike, a forest fire begins to burn and is spreading outward in a shape that is roughly circular. the radius of the circle is modeled by the function r(t) = 2t + 1, where t is the time in minutes and r is measured in meters.

1). write a function for the area burned by the fire directly as a function of t by computing (a ◦ r)(t).

2) find the area of the circular burn after 20 minutes.

1 - meter²

2 - 5,281 meter²

Step-by-step explanation:

We are given that,

Radius of the circle is modeled by the function, , where 't' is the time in minutes.

Part 1: It is required to compute the area of the forest burned.

Since, Area of the circle =

So,

i.e.

i.e.

Thus, the area of the forest burned by the fire is meter²

Part 2: It is required to find the area after 20 minutes of burn.

That is, t = 20 mins.

So substituting, we get,

i.e.

i.e.

i.e.

i.e. meter²

Thus, the area burned after 20 mins of fire is 5,281 meter².