Question

fridays act bellringer
due: friday, september 5, 2025 at 4:00 pm
using extrapolation, predict the height(mm) at day 10

Explanation:

Step1: Assume linear relationship

Since we are using extrapolation and no other information is given, assume a linear relationship between day and height. Let the points be $(x_1,y_1)=(1,2)$ and $(x_2,y_2)=(2,4)$ (from the graph). The slope $m$ of the line is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$.
$m=\frac{4 - 2}{2 - 1}=2$

Step2: Find the equation of the line

The equation of a line in slope - intercept form is $y=mx + b$. Using the point $(1,2)$ and $m = 2$, we substitute into the equation: $2=2\times1 + b$, so $b = 0$. The equation of the line is $y = 2x$.

Step3: Extrapolate to day 10

Substitute $x = 10$ into the equation $y = 2x$.
$y=2\times10=20$

Answer:

20