NZ Level 8 (NZC) Level 3 (NCEA) [In development] 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?

Easy
Approx 3 minutes

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.

### Outcomes

#### M8-4

Use curve fitting, log modelling, and linear programming techniques

#### M8-7

Form and use trigonometric, polynomial, and other non-linear equations

#### 91574

Apply linear programming methods in solving problems

#### 91575

Apply trigonometric methods in solving problems