Question

determining the effect of a new rate of change
plant a:
assume plant b received sunlight, and its rate of change was 1.6 inches a week instead of 1.4 inches per week. would it be taller at 6 weeks?
no. it will be shorter.
no. it will be the same height.
yes. it will be 0.3 inches taller.
yes. it will be 4.5 inches taller.
plant b:
weeks height (in)
2 7.3
3 8.7
4 10.1

Explanation:

Step1: Find initial height of Plant B

We can find the initial - height of Plant B using the slope - intercept form $y = mx + b$. The slope $m$ (rate of change) for the initial data of Plant B can be calculated using two points $(x_1,y_1)=(2,7.3)$ and $(x_2,y_2)=(3,8.7)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{8.7 - 7.3}{3 - 2}=1.4$. Using the point - slope form $y - y_1=m(x - x_1)$ with the point $(2,7.3)$ and $m = 1.4$, we have $y-7.3 = 1.4(x - 2)$. When $x = 0$, $y=7.3-1.4\times2=7.3 - 2.8 = 4.5$.

Step2: Calculate height of Plant B with initial rate at 6 weeks

Using the equation $y=mx + b$ with $m = 1.4$ and $b = 4.5$ and $x = 6$, we get $y_1=1.4\times6+4.5=8.4 + 4.5=12.9$.

Step3: Calculate height of Plant B with new rate at 6 weeks

With a new rate of change $m = 1.6$ and $b = 4.5$ and $x = 6$, we use the equation $y=mx + b$. So $y_2=1.6\times6+4.5=9.6+4.5 = 14.1$.

Step4: Find the difference in heights

The difference $\Delta y=y_2 - y_1=14.1-12.9 = 1.2$. So Plant B will be 1.2 inches taller.

Answer:

Yes. It will be 1.2 inches taller.