Suppose that the population of South Africa was approximately $60,04$ million at the beginning of year $2021,$ and that it follows the Malthusian model approximately, with a growth rate of $1\mathrm{.}24$ percent per year.

$(1\mathrm{.}1)$ When will the population reach $70$ million, if the growth rate does not change?

$(1\mathrm{.}2)$ What does the model predict the population of South Africa to be in the year $2050?$