Question

Nine days ago the area covered by a bread mold was 3 square inches. Now, the mold covers 9 square inches. What is the rate of change in the mold area?

Answer 1

In this particular problem it is given that the area covered by 9 days ago is 3 square inches and in present time it is 3 square inches so total area change is 6 square inches in 9 days. In the question it is asked that the rate of change in mold means that we have changed in area with respect to time so, we have to divide by time taken then simplify and solve further and find the values.

Complete step by step solution:
According to the question it has mentioned the time in which the area of mold is covered.
That means the area of mold covered Nine days ago is 3 square inches and after Nine days it is mentioned that the area of mold is covered 9 square inches.
And we have to calculate change in area of mold occurred in 9 days
To calculate change in area
$\text{change}\,\,\,\text{in}\,\,\,\text{area=Final}\,\,\,\text{area}-\text{intial}\,\,\,\text{area}$
$\text{change}\,\,\,\text{in}\,\,\,\text{area}=(9-3)\,\,\text{square}\,\,\text{inches}$
$\text{change}\,\,\,\text{in}\,\,\,\text{area}=6\,\,\text{square}\,\,\text{inches}$
But according to the question it has mentioned that we have to calculate the rate of change of mold’s area
$\text{The rate of change}\,\,\text{in}\,\,\text{mold }\\!\\!'\\!\\!\text{ s}\,\,\text{area}=\dfrac{\text{change}\,\,\text{in}\,\,\text{area}}{\text{Time}\,\,\text{taken}}$
Time taken by the mold to cover the area in 9 days.
Therefore, the time taken is 9 days.
Change in area is 6 square inches.
Therefore, the rate of change of mold’s area is given by
$\text{The rate of change}\,\,\text{in}\,\,\text{mold }\\!\\!'\\!\\!\text{ s}\,\,\text{area}=\dfrac{(9-3)}{9}$
By simplifying this we get:
$\text{The rate of change}\,\,\text{in}\,\,\text{mold }\\!\\!'\\!\\!\text{ s}\,\,\text{area}=\dfrac{6}{9}$
By reducing fraction we get:
$\text{The rate of change}\,\,\text{in}\,\,\text{mold }\\!\\!'\\!\\!\text{ s}\,\,\text{area}=\dfrac{2}{3}$
Therefore, the rate of change in mold’s area is $\dfrac{2}{3}$ square inches per day.

Note:
In this type of problem the question is asked. Because if the question is asked the rate of change of area. That means we have to calculate the change in area with respect to time. That means we have to divide by time taken. Some students may mistake here that they only calculate the change in area and get the answer that is an incomplete answer but if it is specifically mentioned rate of change then we must divide by the time taken. So, the above solution is preferred for such types of problems.