SOLUTION: 1. Suppose there are 350 million people in the US. If the annual birth rate is 2.3% and the annual death rate is 1.9%, what is the relative annual growth rate (r) of the US Populat

Click here to see ALL problems on Rational-functions

Question 1194800: 1. Suppose there are 350 million people in the US. If the annual birth rate is 2.3% and the annual death rate is 1.9%, what is the relative annual growth rate (r) of the US Population?
a) What will the projected US Population be in 2042 based on an exponential growth model (base e)? Give the model and explain what each part represents.

b) What would happen if birth and death rates were reversed? Clearly explain what type of model this becomes and how the graph changes.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the initial population is 350.
when the growth rate is 2.3% per year and the loss rate is 1.9% per year, the growth factor becomes (1 + .023 - .019) = 1.004.
when the growth rate is 1.9% per year and the loss rate is 2.3% per year, the growth factor becomes (1 + .019 - .023) = (1 - .004) = .996 per year.
for graphing purposes, your formulas are:
y = 1.004 ^ x for a growth factor of 1.004 per year.
y = .996 ^ x for a growth factor of.996 per year.
the first graph shows the results of these 2 equations for the first 5 years.
the second graph shows the results of these 2 equations for the 20th year.
y = 350 * 1.004 ^ x is in red.
y = 350 * .996 ^ x is in blue.
the third display is the supporting data from excel spreadsheet.

let me know if you have any questions.
theo