2.10 Logarithmic scaling and linearizing dataIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 2.10 Logarithmic scaling and linearizing data

1. A researcher studies samples in which the number of cells $N$ ranges from 20 to 3 000 000, so she records $\log_{10}N$ instead of $N$.
   A sample has $\log_{10}N=4.5$. Find $N$, correct to 3 significant figures.2 marks
2. The number of bacteria $N$ in a culture after $t$ hours is modelled by $N=ab^{t}$, where $a$ and $b$ are constants. The relationship between $\ln N$ and $t$ is linear, with gradient $0.35$ and vertical intercept $4.2$.
   Find the value of $a$ and state what it represents.2 marks
3. The orbital period $T$ (days) of a planet and its mean distance $d$ (million km) from the Sun are modelled by $T=kd^{n}$. Data for four planets, with $d$ from 57.9 to 228, give the line of best fit $\log_{10}T=1.5\log_{10}d-0.70$.
   By taking logarithms of $T=kd^{n}$, find the values of $n$ and $k$.3 marks