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I NEED HELP. THE QUESTION IS IN THE PICTURE. IM SO CONFUSED

I NEED HELP. THE QUESTION IS IN THE PICTURE. IM SO CONFUSED-example-1

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a) The given function is expressed as

y = yoe^-0.005t

The rate is - 0.005

Since it is negative, it means that the situation is that of an exponential decay

b) The decay rate is - 0.005

c) The constant, yo represents the initial amount of radioactive isotope

d) When 95% of the sample has decayed, it means that the quantity that has decayed is

95/100 x yo = 0.95yo

This means that when y = 0.95yo, the isotope is no longer useful. To determine the time it will take for 0.95yo to decay, we would substitute y = 0.95yo into the function and solve for t. We have

0.95yo = yoe^-0.005t

0.95yo/ yo = e^-0.005t

0.95 = e^-0.005t

Taking the natural log of both sides of the equation,

ln 0.95 = ln e^-0.005t

By applying the law of logarithms to the right side of the equation,

ln 0.95 = - 0.005t ln e

Recall, ln e = 1

Thus, we have

ln 0.95 = - 0.005t

t = ln 0.95/- 0.005

t = 10.3

It will take 10.3 minutes for 95% of the sample to decay

e) If the student writes the function as

y = yo/e^-0.005t, he is incorrect because the rule of exponents was not applied properly. It should have been

y = yo/e^0.005t

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