Question

due: tuesday, september 2, 2025 at 4:00 pm
using extrapolation, predict the height(mm) at day 5

Explanation:

Step1: Assume linear relationship

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 $(x_4,y_4)=(4,8)$. The general form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{4 - 2}{2 - 1}=2$. Using the point - slope form with the point $(1,2)$: $y - 2=2(x - 1)$, which simplifies to $y = 2x$.

Step2: Substitute $x = 5$

Substitute $x = 5$ into the equation $y = 2x$. So $y=2\times5$.

Answer:

10