Question

Oil is spilled onto a kitchen floor. The area covered by the oil at time t is given by the function A, where A(t) is measured in square centimeters and t
is measured in seconds. Which of the following gives the rate at which the area covered by the oil is changing at time t=10?

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

Oil is spilled onto a kitchen floor. The area covered by the oil at time t is given by the function A, where A(t) is measured in square centimeters and t

is measured in seconds. The rate at which the area covered by the oil is changing at time t = 10 is  A'(10).

Given that:

• The area covered by the oil at time t = A(t)

To determine the rate at which the area covered by the oil is changing with time, we need to differentiate  A(t) with respect to time t.

∴

By differentiation:

$\mathbf{\dfrac{dA}{dt} =A'(t)}$

• The rate at which the area covered with oil is changing is t = 10

∴

$\mathbf{\dfrac{dA}{dt} \Big| _{t=10}=A'(t)\Big|_{t=10}}$

$\mathbf{\dfrac{dA}{dt} =A'(10)}$

Therefore, we can conclude that the rate at which the area covered by the oil is changing at time t=10 is  A'(10).

Learn more about differentiation here:

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