Question

Zinc-65 is a radioactive substance that decays over time. If you start with 100 grams of zinc-65, the amount left after t years can be modeled by the expression 100
7
20
t.
What does the quantity
7
20
t represent?

Answer 1

The expression you provided for the amount of zinc-65 left after \( t \) years appears to contain an error in formatting. It seems you intended to convey an exponential decay formula, possibly of the form:

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

where:
- \( N(t) \) is the amount remaining after time \( t \),
- \( N_0 \) is the initial amount,
- \( k \) is the decay constant,
- \( t \) is time.

Given that you have states “100 7 20 t”, it's likely you are referring to the exponential decay model where \( \frac{7}{20} t \) represents the decay constant multiplied by time.

In the context of a radioactive substance:
- \( \frac{7}{20} \) would represent the decay constant (\( k \)),
- \( t \) is the time in years.

This decay constant indicates the rate at which the substance decays. Specifically, \( k \) relates to the half-life of the substance, which is the amount of time it takes for half of the initial amount of the substance to decay.

In conclusion, the quantity \( \frac{7}{20} t \) represents the exponential decay factor that determines the decrease in mass of zinc-65 over time.