At least one of the answers above is NOT correct. Before expanding to a new country, a company studies the population trends of the region. They find that at the start of 1990 the population of the country was 25 million people. However, the population had increased to 50 million people by the beginning of 1997. Let P(t) give the total population of the country in millions of people, where t =0 is the beginning of 1990. Assume P(t) follows an exponential model of the form P(t) = yo - (b). (a) Translate the information given in the first paragraph above into two data points for the function P(t). List the point that corresponds to 1990 first. PO = 25 P 7 = 50 (b) Next, we will find the two missing parameters for P(t). First, Yo= 25 Then, using the second point from part (a), solve for b. Round to 4 decimal places. b= 1.1041 Note: make sure you have b accurate to 4 decimal places before proceeding. Use this rounded value for b for all the remaining steps. (c) Write the function P(t). P(t) 25 1.1041' (d) Estimate the population of the country at the beginning of 2003 (round to 2 decimal places). According to our model, the population of the country in 2003 is about 27.60 million people. (e) What is the doubling time for the population? In other words, how long will it take for the population to be double what it was at the start of 1990? Solve for t and round to 2 decimal places. The doubling time for the population of the country is about 7 years. Note: You can earn partial credit on this problem.
At least one of the answers above is NOT correct. Before expanding to a new country, a company studies the population trends of the region. They find that at the start of 1990 the population of the country was 25 million people. However, the population had increased to 50 million people by the beginning of 1997. Let P(t) give the total population of the country in millions of people, where t =0 is the beginning of 1990. Assume P(t) follows an exponential model of the form P(t) = yo - (b). (a) Translate the information given in the first paragraph above into two data points for the function P(t). List the point that corresponds to 1990 first. PO = 25 P 7 = 50 (b) Next, we will find the two missing parameters for P(t). First, Yo= 25 Then, using the second point from part (a), solve for b. Round to 4 decimal places. b= 1.1041 Note: make sure you have b accurate to 4 decimal places before proceeding. Use this rounded value for b for all the remaining steps. (c) Write the function P(t). P(t) 25 1.1041' (d) Estimate the population of the country at the beginning of 2003 (round to 2 decimal places). According to our model, the population of the country in 2003 is about 27.60 million people. (e) What is the doubling time for the population? In other words, how long will it take for the population to be double what it was at the start of 1990? Solve for t and round to 2 decimal places. The doubling time for the population of the country is about 7 years. Note: You can earn partial credit on this problem.
Chapter1: Taking Risks And Making Profits Within The Dynamic Business Environment
Section: Chapter Questions
Problem 1CE
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Transcribed Image Text:At least one of the answers above is NOT correct.
Before expanding to a new country, a company studies the population trends of the region. They find that at the start of 1990 the population of the country was 25 million people. However, the
population had increased to 50 million people by the beginning of 1997.
Let P(t) give the total population of the country in millions of people, where t =0 is the beginning of 1990. Assume P(t) follows an exponential model of the form
P(t) = yo - (b).
(a) Translate the information given in the first paragraph above into two data points for the function P(t). List the point that corresponds to 1990 first.
PO = 25
P 7 = 50
(b) Next, we will find the two missing parameters for P(t). First,
Yo= 25
Then, using the second point from part (a), solve for b. Round to 4 decimal places.
b= 1.1041
Note: make sure you have b accurate to 4 decimal places before proceeding. Use this rounded value for b for all the remaining steps.
(c) Write the function P(t).
P(t)
25 1.1041'
(d) Estimate the population of the country at the beginning of 2003 (round to 2 decimal places).
According to our model, the population of the country in 2003 is about 27.60 million people.
(e) What is the doubling time for the population? In other words, how long will it take for the population to be double what it was at the start of 1990? Solve for t and round to 2 decimal places.
The doubling time for the population of the country is about 7 years.
Note: You can earn partial credit on this problem.
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