The question of Matrix
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Every year, 10% of the population of rural Nova Scotia moves to Halifax, and 5% of the population of Halifax moves to rural Nova Scotia. Assume that there are no other effects on these populations.
(a) If the total population of Nova Scotia is 1 million, what will be the population of Halifax and of rural Nova Scotia in the long-term?
(b) Assuming that in the current year, the population of Halifax is 0.4 million, and that of rural Nova Scotia is 0.6 million. Find precise formulas for the values of the populations after n years.
(c) Continuing with the assumptions of (b), after how many years will the population Halifax for the first time surpass the population of rural Nova Scotia?
I am not sure about how to do this question.
I wrote some steps
Rn+1=0.9Rn+0.05Hn
Hn+1=0.95Hn+0.1Rn
(Rn+1) (0.9 0.05) Rn
(Hn+1) (0.1 0.95) Hn
linear-algebra matrices
asked Dec 14 '18 at 0:02
Charlotte CaiCharlotte Cai
11
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add a comment |
$begingroup$
Every year, 10% of the population of rural Nova Scotia moves to Halifax, and 5% of the population of Halifax moves to rural Nova Scotia. Assume that there are no other effects on these populations.
(a) If the total population of Nova Scotia is 1 million, what will be the population of Halifax and of rural Nova Scotia in the long-term?
(b) Assuming that in the current year, the population of Halifax is 0.4 million, and that of rural Nova Scotia is 0.6 million. Find precise formulas for the values of the populations after n years.
(c) Continuing with the assumptions of (b), after how many years will the population Halifax for the first time surpass the population of rural Nova Scotia?
I am not sure about how to do this question.
I wrote some steps
Rn+1=0.9Rn+0.05Hn
Hn+1=0.95Hn+0.1Rn
(Rn+1) (0.9 0.05) Rn
(Hn+1) (0.1 0.95) Hn
linear-algebra matrices
asked Dec 14 '18 at 0:02
Charlotte CaiCharlotte Cai
11
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$begingroup$
Hello, welcome to StackExchange! Your post looks like homework and we do not accept questions without showing some work. What have you tried so far?
$endgroup$
– Lucas Henrique
Dec 14 '18 at 0:04
1
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Hi Lucas, I added some steps but I am not sure how to use the matrix to finish the whole problems
$endgroup$
– Charlotte Cai
Dec 14 '18 at 0:20
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For part a), how do the equations change if you assume that the rural and urban populations stabilize in the long run?
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– saulspatz
Dec 14 '18 at 0:23
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I am not sure. I think it is same as what I wrote?.....
$endgroup$
– Charlotte Cai
Dec 14 '18 at 0:31
$begingroup$
Let $x_n = left[begin{array} \R_n\H_nend{array}right]$. Now you can write a matrix equation of the form x$_{n+1} = A x_n$.
$endgroup$
– Joel Pereira
Dec 14 '18 at 4:46
add a comment |
$begingroup$
Every year, 10% of the population of rural Nova Scotia moves to Halifax, and 5% of the population of Halifax moves to rural Nova Scotia. Assume that there are no other effects on these populations.
(a) If the total population of Nova Scotia is 1 million, what will be the population of Halifax and of rural Nova Scotia in the long-term?
(b) Assuming that in the current year, the population of Halifax is 0.4 million, and that of rural Nova Scotia is 0.6 million. Find precise formulas for the values of the populations after n years.
(c) Continuing with the assumptions of (b), after how many years will the population Halifax for the first time surpass the population of rural Nova Scotia?
I am not sure about how to do this question.
I wrote some steps
Rn+1=0.9Rn+0.05Hn
Hn+1=0.95Hn+0.1Rn
(Rn+1) (0.9 0.05) Rn
(Hn+1) (0.1 0.95) Hn
linear-algebra matrices
asked Dec 14 '18 at 0:02
Charlotte CaiCharlotte Cai
11
$endgroup$
Every year, 10% of the population of rural Nova Scotia moves to Halifax, and 5% of the population of Halifax moves to rural Nova Scotia. Assume that there are no other effects on these populations.
(a) If the total population of Nova Scotia is 1 million, what will be the population of Halifax and of rural Nova Scotia in the long-term?
(b) Assuming that in the current year, the population of Halifax is 0.4 million, and that of rural Nova Scotia is 0.6 million. Find precise formulas for the values of the populations after n years.
(c) Continuing with the assumptions of (b), after how many years will the population Halifax for the first time surpass the population of rural Nova Scotia?
I am not sure about how to do this question.
I wrote some steps
Rn+1=0.9Rn+0.05Hn
Hn+1=0.95Hn+0.1Rn
(Rn+1) (0.9 0.05) Rn
(Hn+1) (0.1 0.95) Hn
linear-algebra matrices
linear-algebra matrices
asked Dec 14 '18 at 0:02
Charlotte CaiCharlotte Cai
11
asked Dec 14 '18 at 0:02
Charlotte CaiCharlotte Cai
11
edited Dec 14 '18 at 0:13
Charlotte Cai
asked Dec 14 '18 at 0:02
Charlotte CaiCharlotte Cai
11
asked Dec 14 '18 at 0:02
Charlotte CaiCharlotte Cai
11
asked Dec 14 '18 at 0:02
Charlotte CaiCharlotte Cai
11
11
$begingroup$
Hello, welcome to StackExchange! Your post looks like homework and we do not accept questions without showing some work. What have you tried so far?
$endgroup$
– Lucas Henrique
Dec 14 '18 at 0:04
1
$begingroup$
Hi Lucas, I added some steps but I am not sure how to use the matrix to finish the whole problems
$endgroup$
– Charlotte Cai
Dec 14 '18 at 0:20
$begingroup$
For part a), how do the equations change if you assume that the rural and urban populations stabilize in the long run?
$endgroup$
– saulspatz
Dec 14 '18 at 0:23
$begingroup$
I am not sure. I think it is same as what I wrote?.....
$endgroup$
– Charlotte Cai
Dec 14 '18 at 0:31
$begingroup$
Let $x_n = left[begin{array} \R_n\H_nend{array}right]$. Now you can write a matrix equation of the form x$_{n+1} = A x_n$.
$endgroup$
– Joel Pereira
Dec 14 '18 at 4:46
add a comment |
$begingroup$
Hello, welcome to StackExchange! Your post looks like homework and we do not accept questions without showing some work. What have you tried so far?
$endgroup$
– Lucas Henrique
Dec 14 '18 at 0:04
1
$begingroup$
Hi Lucas, I added some steps but I am not sure how to use the matrix to finish the whole problems
$endgroup$
– Charlotte Cai
Dec 14 '18 at 0:20
$begingroup$
For part a), how do the equations change if you assume that the rural and urban populations stabilize in the long run?
$endgroup$
– saulspatz
Dec 14 '18 at 0:23
$begingroup$
I am not sure. I think it is same as what I wrote?.....
$endgroup$
– Charlotte Cai
Dec 14 '18 at 0:31
$begingroup$
Let $x_n = left[begin{array} \R_n\H_nend{array}right]$. Now you can write a matrix equation of the form x$_{n+1} = A x_n$.
$endgroup$
– Joel Pereira
Dec 14 '18 at 4:46
$begingroup$
Hello, welcome to StackExchange! Your post looks like homework and we do not accept questions without showing some work. What have you tried so far?
$endgroup$
– Lucas Henrique
Dec 14 '18 at 0:04
$begingroup$
Hello, welcome to StackExchange! Your post looks like homework and we do not accept questions without showing some work. What have you tried so far?
$endgroup$
– Lucas Henrique
Dec 14 '18 at 0:04
1
1
$begingroup$
Hi Lucas, I added some steps but I am not sure how to use the matrix to finish the whole problems
$endgroup$
– Charlotte Cai
Dec 14 '18 at 0:20
$begingroup$
Hi Lucas, I added some steps but I am not sure how to use the matrix to finish the whole problems
$endgroup$
– Charlotte Cai
Dec 14 '18 at 0:20
$begingroup$
For part a), how do the equations change if you assume that the rural and urban populations stabilize in the long run?
$endgroup$
– saulspatz
Dec 14 '18 at 0:23
$begingroup$
For part a), how do the equations change if you assume that the rural and urban populations stabilize in the long run?
$endgroup$
– saulspatz
Dec 14 '18 at 0:23
$begingroup$
I am not sure. I think it is same as what I wrote?.....
$endgroup$
– Charlotte Cai
Dec 14 '18 at 0:31
$begingroup$
I am not sure. I think it is same as what I wrote?.....
$endgroup$
– Charlotte Cai
Dec 14 '18 at 0:31
$begingroup$
Let $x_n = left[begin{array} \R_n\H_nend{array}right]$. Now you can write a matrix equation of the form x$_{n+1} = A x_n$.
$endgroup$
– Joel Pereira
Dec 14 '18 at 4:46
$begingroup$
Let $x_n = left[begin{array} \R_n\H_nend{array}right]$. Now you can write a matrix equation of the form x$_{n+1} = A x_n$.
$endgroup$
– Joel Pereira
Dec 14 '18 at 4:46
add a comment |
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$begingroup$
Hello, welcome to StackExchange! Your post looks like homework and we do not accept questions without showing some work. What have you tried so far?
$endgroup$
– Lucas Henrique
Dec 14 '18 at 0:04
1
$begingroup$
Hi Lucas, I added some steps but I am not sure how to use the matrix to finish the whole problems
$endgroup$
– Charlotte Cai
Dec 14 '18 at 0:20
$begingroup$
For part a), how do the equations change if you assume that the rural and urban populations stabilize in the long run?
$endgroup$
– saulspatz
Dec 14 '18 at 0:23
$begingroup$
I am not sure. I think it is same as what I wrote?.....
$endgroup$
– Charlotte Cai
Dec 14 '18 at 0:31
$begingroup$
Let $x_n = left[begin{array} \R_n\H_nend{array}right]$. Now you can write a matrix equation of the form x$_{n+1} = A x_n$.
$endgroup$
– Joel Pereira
Dec 14 '18 at 4:46