Answer:
Percent of change each year = 5%
Step-by-step explanation:
P.S - The exact question is -
Given - The number of carbon atoms in a fossil is given by the function,
y (x)= [tex]5100(0.95)^{x}[/tex], 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) = [tex]5100(0.95)^{x}[/tex]
Initially, the number of fossils be
y(0) = [tex]5100(0.95)^{0}[/tex] = 5100
After 1 year, The number of fossils be
y(1) = [tex]5100(0.95)^{1}[/tex] = 5100(0.95) = 4845
Now,
Change in 1 year = y(0) - y(1) = 5100 - 4845 = 255
Now,
Percent of chance = [tex]\frac{255}{5100}[/tex] × 100%
= 0.05 × 100%
= 5%
⇒Percent of chance = 5%
∴ we get
Percent of change each year = 5%
