Please show all work/provide explanations as appropriate, including clearly defining any variables that you use in...

Please show all work/provide explanations as appropriate, including clearly defining any variables that you use in the applied problems.

1) According to United Nations estimates ( http://www.worldometers.info/world-population/ ) , the population of the world at the start of 2020 was about 7.795 billion, and it is growing at about 1.05% per year.

a. Find an exponential growth model (i.e. write down an exponential function) that gives the earth’s population in billions as a function of time as measured by number of years after 2020. Be sure to clearly and carefully define your variables.

b. According to the model, what will the world population be in 2030? Solve algebraically as opposed to using a table of values or a graph.

c. Again, according to the model, how long will it take the population to double? Solve this algebraically; that is, do not simply use a table or graph.

d. In what year will the population reach 20 billion? Again, solve without resorting to a table of values or a graph.

2) Refer to the population model you found in problem 1. a. Sketch a graph of your model, displaying at least the next 200 years. You may carefully sketch the graph by hand on graph paper,

b. What is the average rate of change of the world population as described by your model over the next 100 years? (so, from 2020 to 2120, or t = 0 to t = 100)

c. What is the average rate of change from 2020 to 2050?

d. Describe how you could estimate the rate of change of the world population in 2030, and then carry out and show the steps you describe to give an estimate.

Expert Solution

Colby Messinger answered 1 week ago

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