Question

How would I solve the following problem using the exponential formula y = a*b^x ?

The remaining mass of a decaying radioactive isotope is known to
decrease exponentially. In the diagnosis of thyroid disease, an
initial dose of 20 megabequerels (MBq) of the radioactive isotope
iodine-123 (I123) decays to 18 MBq in 2 hours.

a) Find a formula for the amount of I123 left t hours after the initial
dose of 20 MBq was administered.
b) Find the time required for the remaining amount of the isotope
to reach half its initial level.
c) Find the time required for the amount to drop below 1MBq

Answer 1

\[\frac{18}{20}=.9\] loses 10% ever two hours
you can use
\[y=20\times .9^{\frac{t}{2}}\]

Answer 2

for half life you would solve
\[.5=.9^{\frac{t}{2}}\] for \(t\) via
\[\frac{t}{2}=\frac{\ln(.5)}{\ln(.9)}\] or \[t=\frac{2\ln(.5)}{\ln(.9)}\]

Answer 3

last one is similar, but use \[\frac{1}{20}=.9^{\frac{t}{2}}\] as a starting point

Answer 4

i don't understand the way you wrote t/2.... could i also just write that as ^t2?