Question

The population of Salt Lake City, Utah, in 2010 was approximately 1,091,000. From 2010 to 2023, the population of Salt Lake City increased by 11.4%. If an exponential function f can be used to model the population, f(t), of Salt Lake City years after 2010, what equation best defines function f?

Answer 1

Let t = years after 2010. The 13-year growth factor is 1.114, so the annual growth factor is 1.114^(1/13). Thus

f(t) = 1,091,000 · (1.114)^(t/13).

Equivalently,
f(t) = 1,091,000 · (1.114)^(1/13)^t ≈ 1,091,000 · (1.00834)^t
or f(t) = 1,091,000 · e^{(ln 1.114 / 13) t} ≈ 1,091,000 · e^{0.0083077 t}.