The population P in 1995 for a state is given along with r, its annual percentage3 rate of a continuous growth. P=16 millions, r=1.2%
Write the formula f(x) =Pe^yx, where r is in a decimal notation, that models the population in millions x years in 1995.
To write the formula f(x) = Pe^yx, we need to first understand the variables and constants involved.
In this case, P represents the initial population in 1995, which is given as 16 million. The annual percentage growth rate, r, is mentioned as 1.2%. However, for the formula, we need to convert it to decimal notation. To do this, we divide the percentage by 100: r = 1.2 / 100 = 0.012.
Now, the formula f(x) = Pe^yx can be written as:
f(x) = 16e^(0.012x)
Where:
- f(x) represents the population in millions x years after 1995.
- P is the initial population in 1995, which is 16 million.
- e is the mathematical constant approximately equal to 2.71828.
- y is the continuous growth rate in decimal notation, which is 0.012.
- x represents the number of years after 1995.
To find population values for specific years after 1995, substitute the desired value of x into the formula f(x) = 16e^(0.012x) and perform the calculation.