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New Zealand
Level 7 - NCEA Level 2

Applications of Logarithmic Functions (y=klogx+c)

Interactive practice questions

As elevation ($A$A metres) increases, atmospheric air pressure ($P$P pascals) decreases according to the equation $A=15200\left(5-\log P\right)$A=15200(5logP).

Trekkers are attempting to reach the $8850$8850 m elevation of Mt Everest’s summit. When they set up camp at night, their barometer shows a reading of $45611$45611 pascals. How many more vertical metres do they need to ascend to reach the summit?

Give your answer to the nearest metre.

Approx 3 minutes
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The Palermo impact hazard scale is used to rate the potential for collision of an object near Earth. The hazard rating $P$P is given by the equation $P=\log R$P=logR, where $R$R represents the relative risk of collision.

Two asteroids are identified as having a relative risk of collision of $\frac{6}{7}$67 and $\frac{4}{5}$45 respectively.

pH is a measure of how acidic or alkaline a substance is, and the pH scale goes from $0$0 to $14$14, $0$0 being most acidic and $14$14 being most alkaline. Water in a stream has a neutral pH of about $7$7. The pH $\left(p\right)$(p) of a substance can be found according to the formula $p=-\log_{10}h$p=log10h, where $h$h is the substance’s hydrogen ion concentration.

The spread of a virus through a city is modelled by the function $N=\frac{15000}{1+100e^{-0.5t}}$N=150001+100e0.5t, where $N$N is the number of people infected by the virus after $t$t days.



Display the graphs of linear and non-linear functions and connect the structure of the functions with their graphs


Manipulate rational, exponential, and logarithmic algebraic expressions


Apply graphical methods in solving problems


Apply algebraic methods in solving problems

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