IB Mathematics Applications & Interpretation Question Type 1: Scaling Data Appropriately Under the Context Exercises

If variable $y$ ranges from $0$ to $25000\text{ mm}$ and you define $Y=\frac{y}{1000}$ in metres, find the range of $Y$.

An experiment yields the best-fit line $$\ln (P)=-0.2t+3.5$$ Express $P$ as an exponential decay model in the form $P=A{e}^{rt}$, where $A$ and $r$ are constants.

Convert the model $y=5e^{rx}$ into a linear model involving ${\log }_{10}(y)$ and $x$.

A best‐fit line for $\ln (y)$ versus $x$ is given by $$\ln (y)=0.693+0.05x.$$ Determine the parameters $A$ and $r$ of the equivalent exponential model $y=A{e}^{rx}$. [3 marks]

Convert the masses $50\text{ g}$, $1500\text{ g}$ and $25000\text{ g}$ to kilograms. Define $M=\frac{m}{1000}$ where $m$ is in grams. What are the values of $M$?

The exponential model is $$y=5e^{rx}.$$ Show that plotting $\ln (y)$ versus $x$ yields the straight-line equation $\ln (y)=\ln (5)+rx$.

Express the model $y=12e^{-0.5x}$ in the form $\ln (y)=mx+c$ and identify $m$ and $c$.

A process takes times $t=1800$s, $5400$s and $9000$s. A scaled variable $T$ is defined by $T=\frac{t}{3600}$, where $T$ is measured in hours. Calculate the values of $T$.

Given the straight-line fit ${\log }_{10}(y)=1.301+0.02x$, find the equivalent exponential model $y=A{e}^{rx}$.

A company’s monthly revenue ranges from $200,000 to $1,500,000. If $R=\frac{\text{revenue}}{10^6}$ represents the revenue in millions of dollars, find the minimum and maximum values of $R$.

Given the exponential decay model $$N=40e^{-0.5t},$$ find the half‐life $T_{1/2}$ of $N$.