What about Annual Percentage Increase

[studybrat]

The probability problems seem more fun, but this is in the book, so I'm sure it's helpful, esp. in real life instances.

The population of Berryville, Virginia increased from 12,354 to 19,853 in ten years. What was its annual percentage increase in population.

I thought it was supposed to be 19853 - 12354 / 12354 but I think I'm doing something wrong.

Anyone with the expertise?

 

[soroban]

Hello, studybrat!

The population of Berryville, Virginia increased from 12,354 to 19,853 in ten years.
What was its annual percentage increase in population.

I thought it was supposed to be (19853 - 12354)/12354 but I think I'm doing something wrong.

Why would you think that?
. . Is the book's answer different? . . . If so, it's <u>wrong</u>!

You found the <u>amount</u> of increase: 19853 - 12354 = 7499
. . and divided by the <u>original</u> population . . . correct!

 

[studybrat]

Cool!

I guess I was thrown off by the wording; I thought I'd gotten it wrong.

This is great!

 

[Unco]

Isn't that the percentage increase over ten years?

I think a geometric sequence would work.

tn = ar^(n-1)

a = 12354

When t(10) = 19853:
(This is based on the tenth year being 19853, not the 11th)

19853 = 12354 * r^9

r = (19853/12354)^(1/9)

r = 1.054

So the annual percentage increase is (1-1.054)*100 = 5.41% ?