Suppose that the per capita growth rate of a population is $3 \% ;$ that is, if $N(t)$ denotes the population size at time $t$, then
$$\frac{1}{N} \frac{d N}{d t}=0.03$$
Suppose also that the population size at time $t=4$ is equal to
100. Use a linear approximation to compute the population size at time $t=4.1$.