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maths help insanely hard question

5.2The GNP of a country is forecast to grow at 3% per annum and its population is expected to grow at 2% per annum. GNP is currently $20,000 million and the population is 8 million, giving a GNP per capita of $2500. When will the GNP per capita reach $3000?(Hint: assuming continuous growth, the GNP in t years time is 20000e0.03t and the population is 8e0.02t)

5.3An investment of £1 million increases by r% at the end of each year (based upon the value at the start of that year) and after 10 years it is worth £2 million. Find the value of r.Hint: unlike the previous two questions, this one assumes that the value increases in steps rather than continuously. Remember that adding x% is equivalent to multiplying by (1 + x/100)
Original post by anythinggoeshe
5.2The GNP of a country is forecast to grow at 3% per annum and its population is expected to grow at 2% per annum. GNP is currently $20,000 million and the population is 8 million, giving a GNP per capita of $2500. When will the GNP per capita reach $3000?(Hint: assuming continuous growth, the GNP in t years time is 20000e0.03t and the population is 8e0.02t)

5.3An investment of £1 million increases by r% at the end of each year (based upon the value at the start of that year) and after 10 years it is worth £2 million. Find the value of r.Hint: unlike the previous two questions, this one assumes that the value increases in steps rather than continuously. Remember that adding x% is equivalent to multiplying by (1 + x/100)


What have you tried??
Original post by RDKGames
What have you tried??

20000e^0.03t=8000000e^0.02
Original post by anythinggoeshe
20000e^0.03t=8000000e^0.02


OK, that will get you nowhere and shows that you don't even know where to begin. If anything, you should either have 20,000,000 on the LHS or just 8 on the RHS. In the question you are told it's $20,000 million and 8 million.

Firstly, notice where their GNP per capita comes from. It is GNP divided by population.

In the hint you are given that GNP=20000e0.03t\mathrm{GNP} = 20000e^{0.03t} (in millions), and population P=8e0.02tP = 8e^{0.02t} (in millions).

So then GNP per capita is found in the same way, so it's 20000e0.03t8e0.02t\dfrac{20000e^{0.03t}}{8e^{0.02t}}.

You wish to know when this reaches 3000. So make it equal to 3000 and solve for tt.
(edited 5 years ago)
Original post by RDKGames
OK, that will get you nowhere and shows that you don't even know where to begin. If anything, you should either have 20,000,000 on the LHS or just 8 on the RHS. In the question you are told it's $20,000 million and 8 million.

Firstly, notice where their GNP per capita comes from. It is GNP divided by population.

In the hint you are given that GNP=20000e0.03t\mathrm{GNP} = 20000e^{0.03t} (in millions), and population P=8e0.02tP = 8e^{0.02t} (in millions).

So then GNP per capita is found in the same way, so it's 20000e0.03t8e0.02t\dfrac{20000e^{0.03t}}{8e^{0.02t}}.

You wish to know when this reaches 3000. So make it equal to 3000 and solve for tt.

divide 20 mill by 8 to get 2.5 then divide 3000 by 2.5 so e^0.03t/e^0.02t=1.2??? why is it written 200000e and then 8e if they are both in millions
Original post by RDKGames
OK, that will get you nowhere and shows that you don't even know where to begin. If anything, you should either have 20,000,000 on the LHS or just 8 on the RHS. In the question you are told it's $20,000 million and 8 million.

Firstly, notice where their GNP per capita comes from. It is GNP divided by population.

In the hint you are given that GNP=20000e0.03t\mathrm{GNP} = 20000e^{0.03t} (in millions), and population P=8e0.02tP = 8e^{0.02t} (in millions).

So then GNP per capita is found in the same way, so it's 20000e0.03t8e0.02t\dfrac{20000e^{0.03t}}{8e^{0.02t}}.

You wish to know when this reaches 3000. So make it equal to 3000 and solve for tt.

got it right end bit it t=ln1.2/0.01 but only works when its 20000 and 8 but if they are both in millions surely that doesnt make sense coz then its 8 million and then 20000 million but does say in question have it like that
Original post by anythinggoeshe
got it right end bit it t=ln1.2/0.01 but only works when its 20000 and 8 but if they are both in millions surely that doesnt make sense coz then its 8 million and then 20000 million but does say in question have it like that


Original post by anythinggoeshe
divide 20 mill by 8 to get 2.5 then divide 3000 by 2.5 so e^0.03t/e^0.02t=1.2??? why is it written 200000e and then 8e if they are both in millions


You can write them out at 20,000,000,000 and 8,000,000 but at the end of the day, you divide one by the other hence these millions get cancelled out anyway so they have absolutely no effect in this calculation.

So then, I'm not sure why you divided 20 by 8 because you need to divide 20,000 by 8 instead.
Original post by RDKGames
You can write them out at 20,000,000,000 and 8,000,000 but at the end of the day, you divide one by the other hence these millions get cancelled out anyway so they have absolutely no effect in this calculation.

So then, I'm not sure why you divided 20 by 8 because you need to divide 20,000 by 8 instead.

thank you sir. next question:

A country’s gross national product (GNP) is forecast to grow at 3% per annum and its
population is expected to expand at 1.5% per annum. GNP is currently £12,000 million and
the population is 15 million, giving a GNP per capita of £800. When will GNP per capita reach
£1,000?
I think i did this one right. Can i show you picture of my workings
Original post by anythinggoeshe
thank you sir. next question:

A country’s gross national product (GNP) is forecast to grow at 3% per annum and its
population is expected to expand at 1.5% per annum. GNP is currently £12,000 million and
the population is 15 million, giving a GNP per capita of £800. When will GNP per capita reach
£1,000?
I think i did this one right. Can i show you picture of my workings


Go for it, let's see your workings.
Original post by RDKGames
Go for it, let's see your workings.

here
final bit t=ln1.25/0.015?
Original post by anythinggoeshe
here


Looks good.

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