Determine the algebraic modeling a. One type of Iodine disintegrates continuously at a constant rate of displaystyle{8.6}% per day. Suppose the origin

Suman Cole 2020-10-28 Answered
Determine the algebraic modeling a.
One type of Iodine disintegrates continuously at a constant rate of 8.6% per day.
Suppose the original amount, P0, is 10 grams, and let t be measured in days.
Because the Iodine is decaying continuously at a constant rate, we use the model P=P0ekt for the decay equation, where k is the rate of continuous decay.
Using the given information, write the decay equation for this type of Iodine.
b.
Use your equation to determine the half-life ofthis type of Fodine, That is, find ‘out how many days it will take for half of the original amount to be left. Show an algebraic solution using logs.
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Expert Answer

Arham Warner
Answered 2020-10-29 Author has 102 answers
a. The model of the decay equation is given by
P=P0ekt
Here P0=10 grams of iodine
k=rate of continuous rate=8.6% { negative sign implies the decay}
Which implies k=0.086
t is measured in days
Therefore, the decay equation for this type of Iodine is
P=10e0.086t
b. To find the half life of iodine
(i.e)t=? then P=P02=102=5 grams of iodine
P=10e0.086t
substitute P=5 in the above equation
5=10e0.086t
Dividing both sides by 10 we get,
510=e0.086t
e0.086t=12
e0.086t=2
Taking log on both sides we get,
0.086t=loge2
t=loge20.086=0.69310.086=8.05988
Therefore it took 8 days for the iodine reduces to 5 grams
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