This problem is asking for the fractional amount of Strontium-90 remaining as a function of time, based on an exponential decay model. The substance decays at a rate of 2% per year, and at time $t = 0$, 100% of the substance remains.

The general formula for exponential decay is:

$P(t) = P_0 \cdot e^{-kt}$

Where:

• $P(t)$ is the fraction of Strontium-90 remaining after time $t$ years.
• $P_0$ is the initial amount (in this case, 100%, so $P_0 = 1$).
• $k$ is the decay constant.
• $t$ is the time in years.

Since the decay rate is 2% per year, $k$ can be calculated from the fact that after 1 year, $98\%$ (or $0.98$) of the substance remains. Thus:

$P(1) = P_0 \cdot e^{-k \cdot 1} = 0.98$

Solving for $k$:

$e^{-k} = 0.98$ $-k = \ln(0.98)$ $k = -\ln(0.98)$

Now that we have $k$, the function for $P(t)$ becomes:

$P(t) = e^{-k t} = e^{-\ln(0.98) t}$

Thus, the final expression for the fraction of Strontium-90 remaining after $t$ years is:

$P(t) = e^{-\ln(0.98) t}$

Let me know if you'd like more details or if you have any questions!

Here are 5 related questions:

1. How would the equation change if the decay rate was 5% per year?
2. Can you calculate the half-life of Strontium-90 using this model?
3. How much of the substance would remain after 10 years?
4. What is the significance of the decay constant $k$ in this equation?
5. How would the decay function change if Strontium-90 had a constant removal rate instead of an exponential decay?

Tip: Exponential decay models are commonly used in radioactive decay, population decrease, and financial depreciation, where things decline proportionally to their current value.