Answer:
The age of a rock is determined by the function:
[tex]A(t) = A_0 \cdot e^{-0.000002t}[/tex] .....[1]
where,
A(t) be the age of rock after t years
[tex]A_0[/tex] be the initial value of Isotope Q.
t be the number of years.
As per the statement:
A sample originally has 80 grams of Isotope Q, decays, and now has 20 grams of the isotope.
⇒[tex]A_0 = 80[/tex] gram and A(t) = 20 grams
Substitute in [1] we have;
[tex]20 =80 \cdot e^{-0.000002t}[/tex]
Divide both sides by 80 we have;
[tex]0.25 = e^{0.000002t}[/tex]
Taking ln with base e both sides we have;
[tex]\ln 0.25 = -0.000002t[/tex]
⇒[tex]-1.3862943611199 = -0.000002t[/tex]
Divide both sides by 0.000002 we have;
693147.18056 = t
or
t = 693147.18056 years
Therefore, the current age of the sample, in years to the nearest thousand years is, 6,93,147 year
