I am having trouble solving this problem. In 1994, the population of the Las Vegas metropolitan area was about 1,076,000 with an average annual growth rate of 6.5%. Assume this growth rate continues into the future.

I have to estimate the population of Las Vegas each year. I know that the equation should be written in this format, y=ab^x, but what would the equation be? Please help me.

P(n) = Population n years after 1994

= (1,076,000)(1.065)^n

Example: in 1996, after 2 years,
P(n=2) = 1,220,426

in 2007, 13 years after 1994,
P(n=13) = 2,439,817

In case you are curious, the entire population of Clark County NV, which includes Las Vgas, hit 2 million in late 2007. That includes Boulder City and Laughlin, which are well outside the Las Vegas metropolitan area. Therefore the annual growth estimate of 6.5% was too high.

To estimate the population of Las Vegas each year using the given growth rate, we can use the exponential growth formula, which is in the format y = ab^x. In this formula, "y" represents the population size, "a" represents the initial population size, "b" represents the growth factor (1 + growth rate), and "x" represents the number of years.

Based on the information given, we know that the initial population in 1994 was 1,076,000, and the growth rate is 6.5%. Let's calculate the values for "a" and "b" in the equation.

a = 1,076,000 (initial population in 1994)
b = 1 + (growth rate in decimal form) = 1 + 0.065 = 1.065

Now we have the equation y = 1,076,000 * (1.065)^x. This equation will allow you to estimate the population of Las Vegas for any given year, where x represents the number of years from 1994.

For example, if you want to estimate the population in the year 2022 (i.e., 28 years after 1994), substitute x = 28 into the equation:

y = 1,076,000 * (1.065)^28

Using a calculator or spreadsheet, compute the value of the expression to find the estimated population in 2022.