We appreciate your visit to Suppose the population of a country in 1985 was 145 million In 1995 it was 190 million Use the formula tex P A e kt. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To estimate the population of the country in 2005 using the formula [tex]\( P = A e^{kt} \)[/tex], we need to follow these steps:
1. Identify the initial population and time period:
- The initial population in 1985 is given as 145 million. This value will be our [tex]\( A \)[/tex].
- We are estimating the population for the year 2005. Since our starting year is 1985, the time period [tex]\( t \)[/tex] is 20 years (from 1985 to 2005).
2. Estimate the growth rate [tex]\( k \)[/tex]:
- We have information from 1985 to 1995 where the population grew from 145 million to 190 million over 10 years.
- Using the formula for population growth, [tex]\( 190 = 145 e^{10k} \)[/tex], we can find [tex]\( k \)[/tex].
- Solving for [tex]\( k \)[/tex] gives an approximate value of 0.027.
3. Set up the expression for the population in 2005:
- With [tex]\( A = 145 \)[/tex] million, [tex]\( k \approx 0.027 \)[/tex], and [tex]\( t = 20 \)[/tex] years, the expression becomes [tex]\( P = 145 e^{0.027 \times 20} \)[/tex].
4. Conclusion:
- The expression [tex]\( P=145 e^{(0.027)(20)} \)[/tex] is correct for estimating the population of the country in 2005. Therefore, option B is the correct choice.
Using all this information, the population in 2005 is approximately 248.82 million.
1. Identify the initial population and time period:
- The initial population in 1985 is given as 145 million. This value will be our [tex]\( A \)[/tex].
- We are estimating the population for the year 2005. Since our starting year is 1985, the time period [tex]\( t \)[/tex] is 20 years (from 1985 to 2005).
2. Estimate the growth rate [tex]\( k \)[/tex]:
- We have information from 1985 to 1995 where the population grew from 145 million to 190 million over 10 years.
- Using the formula for population growth, [tex]\( 190 = 145 e^{10k} \)[/tex], we can find [tex]\( k \)[/tex].
- Solving for [tex]\( k \)[/tex] gives an approximate value of 0.027.
3. Set up the expression for the population in 2005:
- With [tex]\( A = 145 \)[/tex] million, [tex]\( k \approx 0.027 \)[/tex], and [tex]\( t = 20 \)[/tex] years, the expression becomes [tex]\( P = 145 e^{0.027 \times 20} \)[/tex].
4. Conclusion:
- The expression [tex]\( P=145 e^{(0.027)(20)} \)[/tex] is correct for estimating the population of the country in 2005. Therefore, option B is the correct choice.
Using all this information, the population in 2005 is approximately 248.82 million.
Thanks for taking the time to read Suppose the population of a country in 1985 was 145 million In 1995 it was 190 million Use the formula tex P A e kt. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
