The radius of a circular oil spill after t minutes is given by r ( t ) = √ 25 t . Find the instantaneous rate at which the radius is growing after 31 minutes.

The instantaneous rate at which the radius is growing after 31 minutes is

Explanation:

It is given that the radius of a circular oil spill after t minutes is given by

Simplifying, we have,

The instantaneous rate of change can be determine by differentiating with respect to t.

Thus, we have,

We need to determine the instantaneous rate of the radius after 31 minutes.

Hence, substituting in the above expression, we get,

Substituting the value of , we get,

Multiplying the denominator, we get,

Dividing, we have,

Thus, the instantaneous rate at which the radius is growing after 31 minutes is

65

step-by-step explanation: