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10. The radioactive isotope of lead (Pb-209) decays at a rate proportional to the amount present at time t and has a half-life of 3.3 hours. If 1 gram of this isotope is present initially, (a) how long will it take for 90% of the lead to decay? (Answer: 1= 11 hours) (b) Sketch the mass function.

10. The radioactive isotope of lead (Pb-209) decays at a rate proportional to the amount present at time t and has a half-life of 3.3 hours. If 1 gram of this isotope is present initially, (a) how long will it take for 90% of the lead to decay? (Answer: 1= 11 hours) (b) Sketch the mass function.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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APPLICATION: VARIABLE SEPARABLE

EXPONENTIAL GROWTH/DECAY

10. The radioactive isotope of lead (Pb-209) decays at a rate proportional to the amount present at time i and has a half-life of 3.3 hours. If 1 gram of this isotope is present initially, (a) how long will it take for 90% of the lead to decay? (Answer: 1 = 11 hours) (b) Sketch the mass function. Compound Interest 11. What constant interest rate is required if an initial deposit placed into an account that accrues interest compounded continuously is to double its value in 20 years? Answer: 3% 12. An account is opened with an initial investment of 20,000 dollars. If the account earns continuously compounded interest at an annual rate of 1.25%, how much money is in the account after 15 years? Answer: $24,124.6 13. A person places $120 in a savings account which pays 4 % interest per annum compounded continuously. Find (a) the amount in the account after ten years, and (b) the time required for the account to double in value. Answer: $179 & 17.33 years
Transcribed Image Text:10. The radioactive isotope of lead (Pb-209) decays at a rate proportional to the amount present at time i and has a half-life of 3.3 hours. If 1 gram of this isotope is present initially, (a) how long will it take for 90% of the lead to decay? (Answer: 1 = 11 hours) (b) Sketch the mass function. Compound Interest 11. What constant interest rate is required if an initial deposit placed into an account that accrues interest compounded continuously is to double its value in 20 years? Answer: 3% 12. An account is opened with an initial investment of 20,000 dollars. If the account earns continuously compounded interest at an annual rate of 1.25%, how much money is in the account after 15 years? Answer: $24,124.6 13. A person places $120 in a savings account which pays 4 % interest per annum compounded continuously. Find (a) the amount in the account after ten years, and (b) the time required for the account to double in value. Answer: $179 & 17.33 years
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