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

Suman Cole

Answered question

2020-10-28

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.

Answer & Explanation

Arham Warner

Arham Warner

Skilled2020-10-29Added 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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