Question

9 days ago the area covered by a mold and a piece of bread with three square inches today the mold covers 9 square inches find the change of rate

Answer 1

9 days ago, the mold covered an area of $3in^{2}$.

Today (after 9 days), the mold covers an area of $9in^{2}$.

What is the increase in area? It went from 3 to 9. So the increase is $9-3=6 in^{2}$.

Now, we need to find rate of change. It means to find  how much the area increased every day over the past 9 days. We simply divide the increase (6) by the total number of days (9) to find the rate per day. So we have,

$\frac{6}{9} =\frac{2}{3} in^{2}$

ANSWER: Change of Rate = $\frac{2}{3} in^{2}$ per day

Answer 2

Therate of changeis $\boxed{\frac{{\mathbf{2}}}{{\mathbf{3}}}{\mathbf{ i}}{{\mathbf{n}}^{\mathbf{2}}}}$ per day.

Further explanation:

It is given that 9 days ago, the area covered by a mold and a piece of bread is $3{\text{ i}}{{\text{n}}^2}$.

Consider days as $x$ and the area covered by a mold and a piece of breadas $y$.

Since, the initial value that is first day is consider as 0 and the areacovered by a mold and a piece of bread is $3{\text{ i}}{{\text{n}}^2}$ so the value of ${x_1}$ is $0$ and the value of ${y_1}$ is $3$.

Now, after 9 days ,the area covered by a mold and a piece of bread is $9{\text{ i}}{{\text{n}}^2}$ so the value of ${x_2}$ is $9$  and the value of ${y_2}$ is $9$.

The rate of change is defined as the ratio of the change in $y$ with respect to change in $x$ .

${\text{Rate of change }}= \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}{\text{}}$                        ......(1)

Now, substitute $0$ for ${x_1}$ , $9$ for ${x_2}$, $3$ for ${y_1}$ and $9$ for ${y_2}$ in equation (1) to obtain the rate of change.

$\begin{aligned}{\text{Rate of change }}&= \frac{{9 - 3}}{{9 - 0}}\\ &= \frac{6}{9}\\&=\frac{2}{3}\\\end{aligned}$

Therefore, rate of change is $\dfrac{2}{3}{\text{ i}}{{\text{n}}^2}$.

Thus, the rate of change is $\boxed{\frac{{\mathbf{2}}}{{\mathbf{3}}}{\mathbf{ i}}{{\mathbf{n}}^{\mathbf{2}}}}$ per day.

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Answer Details:

Grade: Junior High School

Subject: Mathematics

Chapter: Surface Area and Volumes

Keywords: Surface area, linear equation, system of linear equations in two variables, largest printed area, derivative, differentiation, mold and piece of bread