The population in January $2003$ was estimated to be about $6\mathrm{.}30$ billion people. Assume that the population will continue to grow exponentially at the rate of about $1\mathrm{.}3\%$ per year. Then the expected$$ population, in billions of$$ people, in t$$ years, is given by the function Upper P left parenthesis t right parenthesis equals $6\mathrm{.}30$ e Superscript $0\mathrm{.}013$ t$,$ where t is the number of years since $2003.$

$$a$)$ Estimate the population in $2010.$

$$b$)$ After how many years will the population$$ double?