Let the exponential growth function is, \(\displaystyle{N}{\left({t}\right)}={N}_{{0}}{e}^{{{k}{t}}}\)

where \(\displaystyle{N}_{{0}}\) and k are the arbitrary constant and t is time.

Since it is given that at t=0 the population of the city was 146,210 so,

\(\displaystyle{146210}={N}_{{0}}{e}^{{{k}{\left({0}\right)}}}\)

\(\displaystyle{N}_{{0}}={146},{210}\)

Also it is given that the population of the city was 217,245 at t=10. so,

\(\displaystyle{217245}={146210}{e}^{{{k}{\left({10}\right)}}}\)

\(\displaystyle{10}^{{k}}={\frac{{{217245}}}{{{146210}}}}\)

\(\displaystyle{10}{k}={\ln{{\left({1.4858}\right)}}}\)

\(\displaystyle{k}={0.03959}\)

Hence, the exponential growth function will be, \(\displaystyle{N}{\left({t}\right)}={146210}{e}^{{{0.03959}{t}}}\)

Substitute t=1 to find the population in the year 2016,

\(\displaystyle{N}{\left({16}\right)}={146210}{e}^{{{0.03959}{\left({16}\right)}}}\)

\(\displaystyle={146210}{e}^{{{0.6335}}}\)

\(\displaystyle={146210}\times{1.884}\)

\(\displaystyle={275460}\)

Hence, the population of the city will be 275,460 in 2016.

where \(\displaystyle{N}_{{0}}\) and k are the arbitrary constant and t is time.

Since it is given that at t=0 the population of the city was 146,210 so,

\(\displaystyle{146210}={N}_{{0}}{e}^{{{k}{\left({0}\right)}}}\)

\(\displaystyle{N}_{{0}}={146},{210}\)

Also it is given that the population of the city was 217,245 at t=10. so,

\(\displaystyle{217245}={146210}{e}^{{{k}{\left({10}\right)}}}\)

\(\displaystyle{10}^{{k}}={\frac{{{217245}}}{{{146210}}}}\)

\(\displaystyle{10}{k}={\ln{{\left({1.4858}\right)}}}\)

\(\displaystyle{k}={0.03959}\)

Hence, the exponential growth function will be, \(\displaystyle{N}{\left({t}\right)}={146210}{e}^{{{0.03959}{t}}}\)

Substitute t=1 to find the population in the year 2016,

\(\displaystyle{N}{\left({16}\right)}={146210}{e}^{{{0.03959}{\left({16}\right)}}}\)

\(\displaystyle={146210}{e}^{{{0.6335}}}\)

\(\displaystyle={146210}\times{1.884}\)

\(\displaystyle={275460}\)

Hence, the population of the city will be 275,460 in 2016.