Answer:
0.01.
Step-by-step explanation:
We have been given that a certain certain quantity has a century decay factor of 0.5. We are asked to find yearly decay factor of the given quantity.
We know that decay factor is in form [tex](1-r)^x[/tex], where r represents decay rate in decimal form and x is time.
We can represent our given information in an equation as:
[tex](1-r)^{100}=0.5[/tex]
Upon taking hundredth root on both sides, we will get:
[tex]\sqrt[100]{(1-r)^{100}}=\sqrt[100]{0.5}[/tex]
[tex]1-r=0.9930924954370359[/tex]
[tex]1-1-r=0.9930924954370359-1[/tex]
[tex]-r=-0.0069075045629641[/tex]
Multiplying both sides by -1, we will get:
[tex]r=0.0069075045629641[/tex]
Upon rounding to two decimal places, we will get:
[tex]r\approx 0.01[/tex]
Therefore, the yearly decay rate is approximately 0.01.
