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 of change per year? Explain how you arrived at your answer.

Answer 1

`\%x=5\%`

Explanation:

From the question we are told that:

Carbon atoms in fossil function

`y=5100(0.95)^x`

Generally the equation a 2 year change is mathematically given by

For
`x=1`

`y_1=5100(0.95)^1\\y_1=4845`

For
`x=2`

`y_2=5100(0.95)^2\\y_2=4602.75`

Generally the equation percentage year changes
`\%x` is mathematically given by

`\%x=(y_1-y_2)/(y_1) *100`

`\%x=(4845-4602.75)/(4845) *100`

`\%x=5\%`

Therefore the percent of change per year is

`\%x=5\%`