Question

For an isotope with a half-life of 36 years, the constant of proportionality is k=0.019
. Find the equation that models the amount of isotope remaining after t years.(1 point)
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Answer 1

To model the amount of an isotope remaining after \( t \) years, we can use the exponential decay formula given by:

\[
N(t) = N_0 e^{-kt}
\]

where:
- \( N(t) \) is the amount of isotope remaining after \( t \) years,
- \( N_0 \) is the initial amount of the isotope,
- \( k \) is the decay constant,
- \( t \) is the time in years,
- \( e \) is the base of the natural logarithm.

In your case, the constant \( k \) is given as \( 0.019 \).

Thus, the equation that models the amount of the isotope remaining after \( t \) years is:

\[
N(t) = N_0 e^{-0.019t}
\]

This equation can be used to determine the remaining quantity of the isotope at any given time \( t \).