A scientist measures the initial amount of Carbon-14 in a substance to be 25 grams.
The relationship between A, the amount of Carbon-14 remaining in that substance, in grams, and t, the elapsed
time, in years, since the initial measurement is modeled by the following equation.
A = 25e 0.00012
In how many years will the substance contain exactly 20 grams (g) of Carbon-14
Give an exact answer expressed as a natural logarithm.
years

1859 years

Step-by-step explanation:

The equation that gives the general decay of a radioactive isotope is:

where

A0 is the initial amount of the isotope at time t = 0

A(t) is the amount of the isotope at time t

is the decay constant of the isotope

For the carbon-14 isotope we have the equation:

Which means that

A0 = 25 g is the initial amount of carbon-14

is the decay constant

We want to find the time t after which the amount of substance left is

A(t) = 20 g

So, by re-arranging the equation for t, we find:

answer: 2530

hope this