a. Explanation Given information : The half-life of bismuth-210, 210 B i , is 5 days. A sample has a mass of 200 mg. Concept Involved: The exponential function will be of the form A = a ⋅ b x where a is the initial amount, b is the growth factor, and A is the amount after x period. The Half-life means the time taken for the initial amount to become half the amount. Calculation: Description Steps With the information provided a = 200 , when t = 5 , the A will be half of a, so A = 100 . Substitute these values to set up an equation 100 = 200 ⋅ b 5 Use symmetric property of identity to rewrite the equation 200 ⋅ b 5 = 100 Dividing by 200 on both sides and simplifying the fraction 200 ⋅ b 5 200 = 100 200 b 5 = 0.5 Taking 5 t h root on both sides to get b and simplifying the left side by using the exponent rule ( a m ) n = a m n ( b 5 ) 1 / 5 = ( 0 b. To determine To find : the amount remaining after t days c. To determine To estimate : the amount remaining after 3 weeks. d. To determine To find : the time required for the mass to be reduced to 1 mg

15th Edition

ISBN: 9781305420878

Author: Stewart

Publisher: CENGAGE L

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Differential Equations

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Chapter 1.4, Problem 31E

To determine

Tofind : the amount remaining after 15 days.

To determine

To find : the amount remaining after t days

To determine

To estimate : the amount remaining after 3 weeks.

To determine

To find : the time required for the mass to be reduced to 1 mg

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Chapter 1.4, Problem 30E

Chapter 1.4, Problem 32E

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Chapter 1 Solutions

BIOCALCULUS:CALCULUS F/LIFE...-W/ACCESS

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Tofind : the amount remaining after 15 days.

Solution Summary: The author explains the exponential function of bismuth-210, 210Bi, where a is the initial amount, growth factor, and amount after x period.

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Tofind : the amount remaining after 15 days.

To find : the amount remaining after t days

To estimate : the amount remaining after 3 weeks.

To find : the time required for the mass to be reduced to 1 mg

Want to see the full answer?

Chapter 1 Solutions