4.07 The natural logarithm

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.

The voltage $V$V in volts across an electrical component decays according to the equation $V=Ae^{-\frac{1}{2}t}$V=Ae−12​t where $A$A is the initial voltage and $t$t is the time in years.

The spread of a virus through a city is modelled 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.