Question

The number of carbon atoms in a fossil is given by the function `y = 5100*.95^x`, where `x` represents the number of years since being discovered. What is the percent of change each year?

Answer 1

percentage annual change is `-5%`

Explanation:

This is a guess!
When looking at the given equation I can not help but think of compound interest. So I am going to convert this into that format.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Within the context of financial interest:
Looking for: `P(1-x)^n`

Where P is the principle sum, `x` is the interest and n is the number of interest cycles (annual)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Given: `y=5100(0.95)^x`

But `0.95=1-0.05` so we have

`y=5100(1-0.05)^x`

But `color(white)(.) 0.05 = 5/100`

So we have `y=5100(1-5/100)^x`

Thus the percentage change each year is `-5%`