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

Answer:

$\%x=5\%$

Step-by-step 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

$\%x=\frac{y_1-y_2}{y_1} *100$

$\%x=\frac{4845-4602.75}{4845} *100$

$\%x=5\%$

Therefore  the percent of change per year is

$\%x=5\%$