(a) Explanation Given information: Strontium-90 has a half life of 28. A sample has a mass of 50 mg initially. Formula used: If a quantity grows by a fixed percent at regular intervals, the pattern can be depicted by these functions. Exponential Growth: y = a (1 + r ) x Exponential Decay: y = a (1 - r ) x Remember that the original exponential formula was y = ab x . You will notice that in these new growth and decay functions, the b value (growth factor) has been replaced either by (1 + r) or by (1 - r). The growth "rate" (r) is determined as b = 1 + r. The decay "rate" (r) is determined as b = 1 – r a = initial value (the amount before measuring growth or decay) r = growth or decay rate (most often represented as a percentage and expressed as a decimal) x = number of time intervals that have passed Calculation: Since m ( t ) = m 0 e k t Now to find the value of k using days for the unit of time assume that a starting mass of m 0 will be reduced to a mass of 1 2 m 0 in 28 days (b) To determine the formula for the mass remaining after 40 days. (c) To determine the rate of decay after 40 days. (d) To determine the time took by the sample to decay to a mass of 2 mg. (e) To determine To Sketch : The graph of the mass function.

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Question

Chapter 3.6, Problem 8E

(a)

To determine

the formula for the mass remaining after t days.

(b)

To determine

the formula for the mass remaining after 40 days.

(c)

To determine

the rate of decay after 40 days.

(d)

To determine

the time took by the sample to decay to a mass of 2 mg.

(e)

To determine

To Sketch : The graph of the mass function.

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Chapter 3.6, Problem 7E

Chapter 3.6, Problem 9E

Chapter 3 Solutions

Biocalculus

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the formula for the mass remaining after t days.

Solution Summary: The author explains the formula for the mass remaining after t days, which is m(t)=50.2t28.

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the formula for the mass remaining after t days.

the formula for the mass remaining after 40 days.

the rate of decay after 40 days.

the time took by the sample to decay to a mass of 2 mg.

To Sketch : The graph of the mass function.

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Chapter 3 Solutions