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1. A sample of a radioactive substance decayed to 97% of its original amount aft

ID: 2912569 • Letter: 1

Question

1. A sample of a radioactive substance decayed to 97% of its original amount after a year. (Round your answers to two decimal places.)

(a) What is the half-life of the substance?

(b) How long would it take the sample to decay to 65% of its original amount?

2. A roast turkey is taken from an oven when its temperature has reached 185°F and is placed on a table in a room where the temperature is 75°F. (Round your answers to the nearest whole number.)

(a) If the temperature of the turkey is 150°F after half an hour, what is the temperature after 60 minutes?

(b) When will the turkey have cooled to 110°?

3. The half-life of cesium-137 is 30 years. Suppose we have a 140-mg sample.

(a) Find the mass that remains after t years.

(b) How much of the sample remains after 140 years? (Round your answer to two decimal places.)

(c) After how long will only 1 mg remain? (Round your answer to one decimal place.)

Explanation / Answer

1) standrad exponential function is

P = Po e^kt

.97Po = Po e^(1k)

k = ln .97

k = -0.03046

a) finding half life of the substance

1/2 = e^ -0.03046 t

t = ln (1/2) /  -0.03046

t = 22.76 year

half life = 22.76 year

b) .65 = e -0.03046^t

t = ln .65 /  -0.03046

t = 14.14

it will take 14.14 years to decay 65% of its original amount