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Mathematics
ramen:

The hourly wage of some Toyota automobile assembly line workers is being increased annually by the same percentage If their wage went from $7.60 to $15.97 in 15 years what is the doubling time?

ramen:

I know how to get the answer of this problem by common sense, but I don't really know how to set up the equation.

AZ:

So it's like similar to a compound interest question, we'll first have to find the growth rate (r) A = P (1 + r/n)^(nt) We went from 7.60 to 15.97 7.60 is our P 15.97 is our A 15 is t and we can say that n = 1 because it's only increasing by r% every year so 15.97 = 7.60(1 + r)^15 can you solve for r?

AZ:

\(\color{#0cbb34}{\text{Originally Posted by}}\) @ramen I know how to get the answer of this problem by common sense, but I don't really know how to set up the equation. \(\color{#0cbb34}{\text{End of Quote}}\) But yeah logically, we can get a rough idea because 15.97 is about twice as much as 7.6 so we know approximately know the doubling time

ramen:

Ohhh Ic ic, yea I was a bit stuck with the filling in the variables part.

ramen:

I got 0.05

AZ:

Let's keep a few more digits so we can get a more accurate number and remember our rule of 70 wants the growth rate as a percentage so multiply it by 100

ramen:

5.07?

AZ:

much better and remember doubling time = 70 / growth rate

ramen:

70/5.07 = 13.8 which rounds to 14 years. Thanks!

AZ:

If they're asking you to round to the nearest year then that's your answer! And no problem!

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