Question

given the least-squares regression line, \\(\widehat{\ln(\text{element})} = 2.305 - 0.101(\text{time})\\), what is the predicted amount of an unstable element that is left after 6 years?
\\(\bigcirc\\) 0.53 gram
\\(\bigcirc\\) 1.699 grams
\\(\bigcirc\\) 5.468 grams
\\(\bigcirc\\) 8.365 grams

Explanation:

Step1: Substitute Time=6 into the equation

$\ln(\text{element}) = 2.305 - 0.101(6)$

Step2: Calculate the right-hand side

$2.305 - 0.606 = 1.699$

Step3: Exponentiate to find element amount

$\text{element} = e^{1.699} \approx 5.468$

Answer:

C. 5.468 grams