Question

Initially 700 milligrams of a radioactive substance was present. After 6 hours the mass had decreased by 9%. Construct an exponential model
A(t) = A0e^kt
for the amount remaining of the decaying substance after t hours. Find the amount remaining after 24 hours.

Answer 1

You're given that \(A_0=700\) and that at \(t=6\), you're left with 91% of the original amount (9% decrease). This means you have
\[0.91=e^{6k}\]
You can find the relative decay factor \(k\), then plug it into the model equation:
\[A(t)=700e^{kt}\]
Once you have this formula, you can find the amount remaining after 24 hours by plugging in \(t=24\):
\[A(24)=700e^{24k}\approx\cdots\]

Answer 2

just want to add one note.
do you see how the Ao cancels?
$$
\large { A(t) = A_oe^{kt}\\
\\ \therefore \\
0.91 A_o=A_oe^{k6}
\\ \therefore \\
0.91=e^{k6}


}
$$

Answer 3

but how would I further solve the problem?

Answer 4

take the natural log of both sides?

Answer 5

yes