In the year 2000, the population of virginia was about 7,400,000. after 2000, the population of virginia grew at a rate of 5.4%. the function f(x)=7,400,000(1.054)^x gives the population x years after 2000.

Question

In the year 2000, the population of virginia was about 7,400,000. after 2000, the population of virginia grew at a rate of 5.4%. the function f(x)=7,400,000(1.054)^x gives the population x years after 2000.
 is the population growing or decaying?
at what rate is the population increasing or decreasing?
what does the 7,400,000 represent?.

GPT-4o mini · Answer

1. **Is the population growing or decaying?** The population of Virginia is growing because the function $ f(x) = 7,400,000(1.054)^x $ models exponential growth. An exponential growth function is characterized by a base greater than 1 (in this case, $ 1.054 $), indicating that as $ x $ (the number of years after 2000) increases, the population will also increase. 2. **At what rate is the population increasing or decreasing?** The population is increasing at a rate of 5.4% per year. This rate reflects the annual growth factor of 1.054 in the function, which means that each year, the population grows by 5.4% of its population from the previous year. 3. **What does the 7,400,000 represent?** The value $ 7,400,000 $ represents the initial population of Virginia in the year 2000. It is the starting point (or y-intercept) of the exponential growth function, indicating the population at $ x = 0 $ (the year 2000).