IB Mathematics Analysis and Approaches Question Type 3: Forecasting Another Value Given a Linear Fit Exercises

In a calibration experiment, the linear fit between temperature $x$ (°C) and resistance $R$ (Ω) is $$R=200+1.5x$$ valid for $0\le x\le 200$. Find $R$ at $150{}^{\circ }\text{C}$.

The linear model for a bacteria culture growth over time $t$ (hours) is $N(t)=100+25t$, based on observations from $t=0$ to $t=12$. Estimate $N(20)$ and comment on the prediction’s reliability.

The linear regression model for the relationship between hours studied $x$ and exam score $y$ is given by $$\text{Score}=40+4.5x$$ based on data for $x$ in the range 2 to 8. Forecast the score for a student who studies 10 hours and comment on the reliability of this prediction.

A study of car speed $x$ (km/h) versus fuel consumption $y$ (L/100 km) yields the linear fit $$\text{Consumption}=5.2+0.03x,$$ for speeds between 40 and 120 km/h. Predict the consumption at 140 km/h and discuss the reliability of this forecast.