3.08 Applications of logarithmic functions
Interactive practice questions
As elevation ($A$A meters) increases, atmospheric air pressure ($P$P pascals) decreases according to the equation $A=15200\left(5-\log P\right)$A=15200(5−logP).
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 meters do they need to ascend to reach the summit?
Give your answer to the nearest meter.
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 modeled by the function $N=\frac{15000}{1+100e^{-0.5t}}$N=150001+100e−0.5t, where $N$N is the number of people infected by the virus after $t$t days.