SOLUTION: Two neighboring towns have had population changes over a ten year period that follow exponential growth or exponential decay patterns.- The population of Town A was 50,000 in 1980.
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Question 703248: Two neighboring towns have had population changes over a ten year period that follow exponential growth or exponential decay patterns.- The population of Town A was 50,000 in 1980. It has increased in population by approximately 5.1% per year.- The population of Town B was 100,000 in 1980. It has experienced a decrease in population of 8.1% per year.
Part A: Write an exponential model to describe the population of Town A. Estimate the population in the year 1988.
Part B: Write an exponential model to describe the population of Town B.
Part C: Estimate the population of town B in the year 2005. Is this a good approximation? Explain why or why not.
Part D: Which model represents exponential growth? Which is a model of exponential decay? Explain why exponential growth or exponential decay models can be used for this data.
Part E: Approximately how many years would it take the population of Town A to double? Determine the solution algebraically.
Part F: In how many years would the population of Town B decrease by 25%? Determine the solution algebraically.
Part G: Determine the year when the towns would have approximately the same population. Use two different methods. Explain why using an algebraic method would be difficult here.
Can someone please solve this, my brother is learning this concept right now, so I found this practice problem online for him, but I don't know the right answers. If I knew the right answers, I could better instruct him how to do it. Thanks so much!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Two neighboring towns have had population changes over a ten year period that follow exponential growth or exponential decay patterns.- The population of Town A was 50,000 in 1980. It has increased in population by approximately 5.1% per year.- The population of Town B was 100,000 in 1980. It has experienced a decrease in population of 8.1% per year.
Part A: Write an exponential model to describe the population of Town A. Estimate the population in the year 1988.
P(x) = 50,000*(1+0.051)^x where x is number of years after 1980
P(8) = 50,000*(1.051)^8 is approximately 74,438
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Part B: Write an exponential model to describe the population of Town B.
P(x) = 100,000*(1-0.081)^x
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Part C: Estimate the population of town B in the year 2005. Is this a good approximation? Explain why or why not.
P(5) = 100,000*(0.919)^5 = 65,551
Looks good to me.
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Part D: Which model represents exponential growth?:::: A
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Which is a model of exponential decay?::: B
Explain why exponential growth or exponential decay models can be used for this data.
A is increasing exponentially ; B is decreasing exponentially.
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Part E: Approximately how many years would it take the population of Town A to double? Determine the solution algebraically.
Solve: (1.051)^x = 2
x = log(2)/log(1.051) is approximately 14 years
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Part F: In how many years would the population of Town B decrease by 25%? Determine the solution algebraically.
Solve (0.919)^x = 0.75
x = log(0.75)/log(0.919) is more than 3 years and less than 4
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Part G: Determine the year when the towns would have approximately the same population. Use two different methods. Explain why using an algebraic method would be difficult here.
50,000(1.051)^x = 100,000(0.919)^x
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(1.051/0.919)^x = 2
x = log(2)/log(1.144) is approximately 5.165 or more than 5 years; less than 6
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Cheers,
Stan H.
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