Salt Lake City, Utah Determine its population on January 1st of a certain year. Write an
exponential function to represent the city’s population, y, based on the
number of years that pass, x after a period of exponential growth. Describe
the variables and numbers that you used in your equation
To determine the population of Salt Lake City, Utah on January 1st of a certain year, we need to know the population on a specific date and the growth rate of the city's population. Without this information, it is not possible to provide an accurate exponential function to represent the city's population.
However, I can explain the variables and numbers typically used in an exponential growth function for population.
In a general form, an exponential growth function for population can be written as:
y = a * (1 + r)^x
Where:
- y represents the population at a given time (in this case, January 1st of a certain year).
- a is the initial population at a specific known time (e.g., January 1st of a known year).
- r is the growth rate of the population, expressed as a decimal. If r is positive, it indicates population growth, while a negative r would represent population decline.
- x represents the number of years that have passed since the known time (e.g., x=0 would represent the known population on January 1st of the known year).
To create a specific exponential growth function for Salt Lake City's population, we would need data on the city's population at a known date and the growth rate. With this information, we could determine the values of a and r to substitute into the exponential growth equation.