Question 9
A radioactive substance decays at a continuous rate of $14.9\mathrm{\%}$ per day. After 8 days, what amount of th substance will be left if you started with $300\mathrm{mg}$ ?
(a) First write the rate of decav in derimal form. $r=$
(b) Now calculate the remaining amount of the substance. Round your answer to two decimal places.
Question Help: @Messageinstuigar:
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Step 1 ：First, we need to convert the decay rate from percentage to decimal form. The decay rate is given as 14.9%, so in decimal form it is $-0.149$.

Step 2 ：Next, we use the exponential decay formula, which is $A=P\ast e^{rt}$, where $A$ is the amount of substance after time $t$, $P$ is the initial amount of substance, $r$ is the decay rate, and $t$ is the time.

Step 3 ：In this case, $P=300$ mg, $r=-0.149$, and $t=8$ days.

Step 4 ：Substituting these values into the formula, we get $A=300\ast e^{-0.149\ast 8}$.

Step 5 ：Calculating this gives us $A=91.08402887270195$ mg.

Step 6 ：Rounding this to two decimal places, we get $A=91.08$ mg.

Step 7 ：So, the remaining amount of the substance after 8 days is approximately $\boxed{{\displaystyle 91.08\text{mg}}}$.