Question

The number of carbon atoms in a fossil is given by the function y= 5100(0.95)^x where x represents the number of years since being discovered what is the percent change each year? Explain your answer.

Answer 1

Answer:

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

.

0.05

=

5

100

So we have

y

=

5100

(

1

−

5

100

)

x

Thus the percentage change each year is

−

5

%

Step-by-step explanation: