Final answer:
The effective annual growth rate for a quantity with a half-life of 14 years is calculated using the decay constant and the exponential decay formula, resulting in a decay rate of -4.9% per year.
Step-by-step explanation:
The effective annual growth rate when a quantity has a half-life of 14 years can be determined using the equation N = Noe−λt, where λ is the decay constant, and e is the base of the natural logarithm. Given that a half-life corresponds to the time it takes for a quantity to reduce to half its initial value, we can use λ = −0.693 / t1/2, where t1/2 is the half-life of the quantity. Substituting the half-life of 14 years into the equation gives us λ = −0.693 / 14. To convert the decay constant into an effective annual growth rate, we use the definition that the effective annual growth rate (EAR) is EAR = eλ −1 expressed as a percentage.
Plugging in the calculated value of λ, we get EAR = 2.71828(−0.693 / 14) −1. After calculation, the effective annual growth rate is found to be -4.9% (rounded to one decimal place), indicating a decay since the percentage is negative.