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(a) The total reserves of a non-renewable resource are 400 million tons. Annual consumption, currently 25 million tons per year, is expected to rise by 1% each year. After how many years will the reserves be exhausted? (b) Instead of increasing by 1% per year, suppose con- sumption was decreasing by a constant percentage per year. If existing reserves are never to be ex- hausted, what annual percentage reduction in con- sumption is required?

(a) The total reserves of a non-renewable resource are 400 million tons. Annual consumption, currently 25 million tons per year, is expected to rise by 1% each year. After how many years will the reserves be exhausted? (b) Instead of increasing by 1% per year, suppose con- sumption was decreasing by a constant percentage per year. If existing reserves are never to be ex- hausted, what annual percentage reduction in con- sumption is required?

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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41. 8+8 (x- pounded annually. 42. 5+5 (z' – 8) + 5 (z – 8)° + 5 (z' – 8)° + .. (a) How much me - In Problems 43-45, for the given value of x determine whether the infinite geometric series converges. If so, find (i) On the ni (ii) On the da its sum: (b) What was the day it was sign 3+3 cos x +3 (cos x) +3 (cos x) + --.. 52. Peter wishes to crea can draw $20,000 w at each anniversary 43. x = 0 44. x 27/3 45. x T plans to retire 20 year he make today if he ca pounded annually? 46. Bill invests $200 at the start of each month for 24 months, starting now. If the investment yields 0.5% per month, compounded monthly, what is its value at the end of 24 months? 53. In 2013, the quantity 17.9 million tonnes an annually. By the end 47. Once a day, eight tons of pollutants are dumped into a bay. Of this, 25% is removed by natural processes each day. What happens to the quantity of pollutants in the bay over time? Give the long-run quantity right after a dump. copper reserves were (a) Write and sum a s copper mined in the quantity minec at 0.025% per year (b) In what year are th 48. (a) The total reserves of a non-renewable resource are 400 million tons. Annual consumption, currently 25 million tons per year, is expected to rise by 1% each year. After how many years will the reserves (c) How does the sum the integral " 17.5 be exhausted? (b) Instead of increasing by 1% per year, suppose con- sumption was decreasing by a constant percentage per year. If existing reserves are never to be ex- hausted, what annual percentage reduction in con- sumption is required? 54. This problem shows anc run ampicillin level. (Se ampicillin levels off to c taken. Six hours later, ri will be less ampicillin ir ity has been reached, the been excreted is exactly 49. A repeating decimal can always be expressed as a frac- tion. This problem shows how writing a repeating dec- imal as a geometric series enables you to find the frac- tion. more tablet raises the lev solve for Q. 55. On page 481, you saw hoL mg of ampicillin in the bo (a) Write the repeating decimal 0.232323. as a ge- DIDIC #0497 MAR 25
Transcribed Image Text:41. 8+8 (x- pounded annually. 42. 5+5 (z' – 8) + 5 (z – 8)° + 5 (z' – 8)° + .. (a) How much me - In Problems 43-45, for the given value of x determine whether the infinite geometric series converges. If so, find (i) On the ni (ii) On the da its sum: (b) What was the day it was sign 3+3 cos x +3 (cos x) +3 (cos x) + --.. 52. Peter wishes to crea can draw $20,000 w at each anniversary 43. x = 0 44. x 27/3 45. x T plans to retire 20 year he make today if he ca pounded annually? 46. Bill invests $200 at the start of each month for 24 months, starting now. If the investment yields 0.5% per month, compounded monthly, what is its value at the end of 24 months? 53. In 2013, the quantity 17.9 million tonnes an annually. By the end 47. Once a day, eight tons of pollutants are dumped into a bay. Of this, 25% is removed by natural processes each day. What happens to the quantity of pollutants in the bay over time? Give the long-run quantity right after a dump. copper reserves were (a) Write and sum a s copper mined in the quantity minec at 0.025% per year (b) In what year are th 48. (a) The total reserves of a non-renewable resource are 400 million tons. Annual consumption, currently 25 million tons per year, is expected to rise by 1% each year. After how many years will the reserves (c) How does the sum the integral " 17.5 be exhausted? (b) Instead of increasing by 1% per year, suppose con- sumption was decreasing by a constant percentage per year. If existing reserves are never to be ex- hausted, what annual percentage reduction in con- sumption is required? 54. This problem shows anc run ampicillin level. (Se ampicillin levels off to c taken. Six hours later, ri will be less ampicillin ir ity has been reached, the been excreted is exactly 49. A repeating decimal can always be expressed as a frac- tion. This problem shows how writing a repeating dec- imal as a geometric series enables you to find the frac- tion. more tablet raises the lev solve for Q. 55. On page 481, you saw hoL mg of ampicillin in the bo (a) Write the repeating decimal 0.232323. as a ge- DIDIC #0497 MAR 25
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