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 ƒ can be to model the population, f(t) , of Salt Lake City & years after 2010, which of the following equations best defines function ƒ?

A f(t)=1,091,000(1.114)ᵗ/¹³
B f(t)=1,091,000(1.114)ᵗ
C f(t)=1,091,000(11.4)ᵗ/¹³
D f(t)=1,091,000( (1.114)/13 )ᵗ

Answer 1

The equation that best defines the exponential function ƒ(t) to model the population of Salt Lake City from 2010 to 2023 is f(t) = 1,091,000(1.114)^(t/13).

Step-by-step explanation:

The equation that best defines the exponential function ƒ(t) to model the population of Salt Lake City over the years is: f(t) = 1,091,000(1.114)^(t/13) (Option A).

The equation represents the initial population of 1,091,000 multiplied by the growth factor of 1.114 raised to the power of (t/13), where t is the number of years since 2010. By substituting different values of t into the equation, we can calculate the population at different points in time.

For example, if we substitute t = 13 (corresponding to the year 2023), we get:

f(13) = 1,091,000(1.114)^(13/13) = 1,091,000(1.114) = 1,215,374