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Standard level

4.07 The natural logarithm

Interactive practice questions

Solve for $x$x, rounding to two decimal places:

$\ln31=x$ln31=x

Hard
< 1min

The population $P$P of a city increases according to the formula $P=3000e^{kt}$P=3000ekt where $t$t is measured in years and $k$k is a constant.

Medium
7min

The voltage $V$V in volts across an electrical component decays according to the equation $V=Ae^{-\frac{1}{2}t}$V=Ae12t where $A$A is the initial voltage and $t$t is the time in years.

Medium
3min

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.

Medium
5min
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