Writing and evaluating a function modeling continuous exponential growt.
$\Longrightarrow \mathrm{t}^{\mathrm{t}}$
A specific radioactive substance follows a continuous exponential decay model. It has a half-life of 16 hours. At the start of the experiment, $36.2 \mathrm{~g}$ is present.
(a) Let $t$ be the time (in hours) since the start of the experiment, and let $y$ be the amount of the substance at time $t$.
Write a formula relating $y$ to $t$. Use exact expressions to fill in the missing parts of the formula. Do not use approximations.
\[
y=\square(\mathbb{D})
\]
(b) How much will be present in 9 hours?
Do not round any intermediate computations, and round your answer to the nearest tenth.
Explanition
Check

Step 1 ：The problem is asking for a formula that models the decay of a radioactive substance over time. The general formula for exponential decay is \(y = a(0.5)^{t/h}\), where \(a\) is the initial amount, \(t\) is the time, and \(h\) is the half-life. In this case, \(a = 36.2\) and \(h = 16\). So, the formula becomes \(y = 36.2(0.5)^{t/16}\).

Step 2 ：For part (b), we need to substitute \(t = 9\) into the formula to find out how much of the substance will be present after 9 hours.

Step 3 ：By substituting \(t = 9\) into the formula, we get \(y = 36.2(0.5)^{9/16}\).

Step 4 ：Calculating the above expression, we get \(y \approx 24.5\).

Step 5 ：Final Answer: (a) The formula relating \(y\) to \(t\) is \(y = 36.2(0.5)^{t/16}\). (b) The amount of the substance that will be present after 9 hours is approximately \(\boxed{24.5}\) g.