Question

The number of carbon atoms in a fossil is given by the function, = 5,100(0.95),wherexrepresentsthenumberofyearssincebeing discovered.

Answer 1

Percent of change each year = 5%

Explanation:

P.S - The exact question is -

Given - The number of carbon atoms in a fossil is given by the function,

y (x)=
`5100(0.95)^(x)`, where x represents the number of years since

being discovered.

To find - What is the percent of change each year? Explain how you arrived

at your answer

Proof -

Given that, the number of carbon atoms in a fossil is y(x) =
`5100(0.95)^(x)`

Initially, the number of fossils be

y(0) =
`5100(0.95)^(0)` = 5100

After 1 year, The number of fossils be

y(1) =
`5100(0.95)^(1)` = 5100(0.95) = 4845

Now,

Change in 1 year = y(0) - y(1) = 5100 - 4845 = 255

Now,

Percent of chance =
`(255)/(5100)` × 100%

= 0.05 × 100%

= 5%

⇒Percent of chance = 5%

∴ we get

Percent of change each year = 5%