Writing and evaluating a function modeling continuous exponential growt.
$⟹{\mathrm{t}}^{\mathrm{t}}$
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.
$$y=◻(\mathbb{D})$$
(b) How much will be present in 9 hours?
Do not round any intermediate computations, and round your answer to the nearest tenth.
Explanition
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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 $\boxed{{\displaystyle 24.5}}$ g.