# Thread: [Easy] Need some help solving this

1. ## [Easy] Need some help solving this

Here is the question

The Swedish krona's currency has gone down by half during a 15-year period. Calculate the yearly procentual decline, if we assume the decline has been the same each year.

This is what I have come up with;

x^15 = ?
How do I write "a half" when I don't know what it is a half of?
The answer to this should be 4,5%

2. Originally Posted by Hanga
Here is the question

The Swedish krona's currency has gone down by half during a 15-year period. Calculate the yearly procentual decline, if we assume the decline has been the same each year.

This is what I have come up with;

x^15 = ?
How do I write "a half" when I don't know what it is a half of?
The answer to this should be 4,5%
$\displaystyle (1 + x)^(15) = 0.5$
Take the natural log of both sides:
$\displaystyle 15 * ln(1 + x) = 0.5$

Can you solve from here?

3. Originally Posted by mathceleb
$\displaystyle (1 + x)^(15) = 0.5$
Take the natural log of both sides:
$\displaystyle 15 * ln(1 + x) = 0.5$

Can you solve from here?
No i'm very sorry but I can't because i've never used the "In" command before I will come across the in command in a few pages, though it is not applied in this particular math problem.

4. It stands for the Natural Log. Essentially, what power do you have to raise e, which is Euler's constant to, to get a number.

Natural logarithm - Wikipedia, the free encyclopedia

That's how you solve for the percentage in this problem. I worked it through, and it comes up to t he answer you give.

Do you want to research the link, or have me finish the math?

5. Hello, Hanga!

No logs needed . . .

The Swedish krona's currency has gone down by half during a 15-year period.
Calculate the yearly percent decline,
if we assume the decline has been the same each year.
The original amount is irrelevant.

Let $\displaystyle r$ = annual rate of devaluation (percent).

Suppose the original value of the krona is $\displaystyle X$ monetary units.

In the first year, the krona has lost $\displaystyle rX$ of its value.
. . Its value is: .$\displaystyle X - rX \:=\:X(1-r)$ units.

In general, in $\displaystyle n$ years, the value is reduced to: .$\displaystyle X(1-r)^n$ units.

We are told that in 15 years, the value is: .$\displaystyle 0.5X$

There is our equation: .$\displaystyle X(1 - r)^{15} \:=\:0.5X$

Divide by $\displaystyle X\!:\;\;(1-r)^{15} \:=\:0.5\quad\hdots$ .
(see?)

Take the 15th root: .$\displaystyle 1 - r \:=\:(0.5)^{\frac{1}{15}}$

. . and we have: .$\displaystyle r \:=\:1 - (0.5)^{\frac{1}{15}} \:=\:0.045158396$

Therefore: .$\displaystyle r \:\approx\:4.5\%$

6. Originally Posted by Soroban
Hello, Hanga!

No logs needed . . .

The original amount is irrelevant.

Let $\displaystyle r$ = annual rate of devaluation (percent).

Suppose the original value of the krona is $\displaystyle X$ monetary units.

In the first year, the krona has lost $\displaystyle rX$ of its value.
. . Its value is: .$\displaystyle X - rX \:=\:X(1-r)$ units.

In general, in $\displaystyle n$ years, the value is reduced to: .$\displaystyle X(1-r)^n$ units.

We are told that in 15 years, the value is: .$\displaystyle 0.5X$

There is our equation: .$\displaystyle X(1 - r)^{15} \:=\:0.5X$

Divide by $\displaystyle X\!:\;\;(1-r)^{15} \:=\:0.5\quad\hdots$ .
(see?)

Take the 15th root: .$\displaystyle 1 - r \:=\0.5)^{\frac{1}{15}}$

. . and we have: .$\displaystyle r \:=\:1 - (0.5)^{\frac{1}{15}} \:=\:0.045158396$

Therefore: .$\displaystyle r \:\approx\:4.5\%$

wow... you just made my head explode I know you guys are like super good at math and stuff and I try to come by and i'm doing my very best, but that explenation is like the most advanced thing i've ever seen I wish to learn that in the future, belive me I do
This is an A grade question (the VERY EASY one) and the answer to the first question was extremly easy. Let me show you;

A prognosis says that our electicity use will quadruple in the next 25 years. By how many percent per year will the electicity usage go up?

We know we have 25. We know it will quadruple (4) but we don't know how many percent it will go up with.

x^25 = 4
(x^25)1/25 = 4^1/25
x = 4^1/25
x = 1,057 which is almost 5,7%

Thats how easy it should be :P
Pretty awsome to see how good I could get at math though.. I really look up to you guys and girls

7. [The Swedish krona's currency has gone down by half during a 15-year period. Calculate the yearly procentual decline, if we assume the decline has been the same each year.]

So here is what I have tried;

x^15 = x / 2
2x^15 = x
2 = x / x^15
2 = x^14
2^1/14 = x
x = 1.057

Wrong....

x^15 = 0.5
x = 0.5^1/15
x = 0,9548

Wrong.... but It could be right because x (is almost) = 0,955. Might be that
1-0.955 = 0.045 = 45%.
aha.. that would be that the diffirence, thus the DECLINE would be 45% not the incline. The diffirence might be calculated from the aspects of 100%... someone please correct me on this one

8. Originally Posted by Hanga
[The Swedish krona's currency has gone down by half during a 15-year period. Calculate the yearly procentual decline, if we assume the decline has been the same each year.]

So here is what I have tried;

x^15 = x / 2
2x^15 = x
2 = x / x^15
2 = x^14
2^1/14 = x
x = 1.057

Wrong....

x^15 = 0.5
x = 0.5^1/15
x = 0,9548

Wrong.... but It could be right because x (is almost) = 0,955. Might be that
1-0.955 = 0.045 = 45%.
aha.. that would be that the diffirence, thus the DECLINE would be 45% not the incline. The diffirence might be calculated from the aspects of 100%... someone please correct me on this one
In your post above, you subtracted 1, you do that here as well, as you want the effective rate of change.

9. Originally Posted by mathceleb
In your post above, you subtracted 1, you do that here as well, as you want the effective rate of change.
So the math problem should look like this;

1 - x^15 = 0.5

?

10. Look at how Soroban wrote it out, that is the standard for which we want to follow.