Question

chemistry: section 203 > week 4 september 2 - 5, 2025 thursday, september 4, 2024 pre - ap che thursadys act bellringer due: thursday, september 4, 2025 at 4:00 pm using extrapolation, predict the height(mm) at day 7

Explanation:

Step1: Assume linear relationship

Since no other information is given, assume a linear relationship between day and height. Let the points be $(x_1,y_1)=(1,2)$ and $(x_2,y_2)=(2,4)$ and $(x_3,y_3)=(3,6)$ and $(x_4,y_4)=(4,8)$ and $(x_5,y_5)=(5,10)$. The general form of a line is $y = mx + b$. First, find the slope $m$. Using two - points $(x_1,y_1)$ and $(x_2,y_2)$, $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{4 - 2}{2 - 1}=2$.

Step2: Find the y - intercept

Substitute $m = 2$ and the point $(1,2)$ into $y=mx + b$. So, $2=2\times1 + b$, which gives $b = 0$. The equation of the line is $y = 2x$.

Step3: Predict height at day 7

Substitute $x = 7$ into the equation $y = 2x$. Then $y=2\times7 = 14$.

Answer:

14