I know that year 2010, the population is 38.447 million and year 2011, the population is 38.935 million.

The formula given: A=36.1e^(0.0126*t)

Determine the population in 2010 and 2011 to nearest thousand people. Use these values to determine the increase in population to the nearest thousand people over this one year period.
What is this as an annual percentage growth rate with 2 digits after the decimal point?

I subtracted the populations and got 488,000 people.

Then I took that number and divided by 38.935 million to get the decimal answer and after that, I multiplied the decimal by 100 to get the annual percentage growth rate of 1.25%

Would that be the correct answer?

To determine the population in 2010 and 2011 using the given formula A = 36.1e^(0.0126*t), we can substitute the years 2010 and 2011 into the formula and round the results to the nearest thousand people.

For 2010:
A = 36.1e^(0.0126 * 2010)
A ≈ 36.1e^(25.326)
A ≈ 167873446.7

Rounding to the nearest thousand, the population in 2010 is approximately 167,873 thousand people (or 167.9 million people).

For 2011:
A = 36.1e^(0.0126 * 2011)
A ≈ 36.1e^(25.389)
A ≈ 169149497.5

Rounding to the nearest thousand, the population in 2011 is approximately 169,149 thousand people (or 169.1 million people).

To determine the increase in population over this one year period, we subtract the 2010 population from the 2011 population:

169,149 - 167,873 = 1,276.

Rounding to the nearest thousand, the increase in population is approximately 1,276 thousand people (or 1.3 million people).

To calculate the annual percentage growth rate, we can use the formula:

Growth rate = ((final value - initial value) / initial value) * 100.

In this case, the initial value is the population in 2010 and the final value is the population in 2011.

Growth rate = ((169,149 - 167,873) / 167,873) * 100
Growth rate ≈ (1,276 / 167,873) * 100
Growth rate ≈ 0.761 * 100
Growth rate ≈ 76.1%

Therefore, the annual percentage growth rate to two decimal places is 76.1%.