Question

A certain quantity has a century decay factor of 0.5. What is its yearly decay factor? (Round your answer to two decimal places.)

Answer 1

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 $(1-r)^x$, where r represents decay rate in decimal form and x is time.

We can represent our given information in an equation as:  

$(1-r)^{100}=0.5$

Upon taking hundredth root on both sides, we will get:

$\sqrt[100]{(1-r)^{100}}=\sqrt[100]{0.5}$

$1-r=0.9930924954370359$

$1-1-r=0.9930924954370359-1$

$-r=-0.0069075045629641$

Multiplying both sides by -1, we will get:

$r=0.0069075045629641$

Upon rounding to two decimal places, we will get:

$r\approx 0.01$

Therefore, the yearly decay rate is approximately 0.01.