Question

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?

Answer 1

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.

Answer 2

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?

Answer 3

\(\color{#0cbb34}{\text{Originally Posted by}}\) @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

Answer 4

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

Answer 5

I got 0.05

Answer 6

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

Answer 7

5.07?

Answer 8

much better and remember

doubling time = 70 / growth rate

Answer 9

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

Answer 10

If they're asking you to round to the nearest year then that's your answer!

And no problem!