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7:40 PM Sat Mar 21 * 100%| dN dt 0.2572N. a. Let No represent the amount of gold-198 present at t = 0. Find an exponential function that models this situation. b. Suppose 10 mg of gold-198 is present at 1 = 0. How much will remain after 1 week? c. What is the rate of change of the amount of gold-198 after 1 week? d. After how many days will half of the original 10 mg of gold-198 remain? e. After how many days will 85% of the gold-198 have decayed? 6. Radioactive decay. Chromium-51 has a decay rate of 2.5% per day. The rate of change of an amount N of chromium-51 after t days is given by dN dt – 0.025N. a. Let No represent the amount of chromium-51 present at i = 0. Find an exponential function that models this situation. b. Suppose 20 mg of chromium-51 is present at 1 = 0. How much will remain after 30 days? c. What is the rate of change of the amount of chromium-51 after 30 days? d. After how many days will half of the original 20 mg of chromium-51 remain? e. After how many days will 95% of the chromium-51 have decayed away? 7. Population decay. Since 1990, the population of Gary, Indiana, has been decreasing by 1.87% per year. The rate of change of the city's population P, t years after 1990, is given by 0.0187P. dt a. In 1990, the population of Gary was 116,646. (Source: U.S. Census Bureau.) Find an exponential function that models this situation. b. Estimate the population of Gary in 2025. c. What is the rate of change of the population of Gary in 2025? d. After how many years will the population of Gary be half of what it was in 1990?

7:40 PM Sat Mar 21 * 100%| dN dt 0.2572N. a. Let No represent the amount of gold-198 present at t = 0. Find an exponential function that models this situation. b. Suppose 10 mg of gold-198 is present at 1 = 0. How much will remain after 1 week? c. What is the rate of change of the amount of gold-198 after 1 week? d. After how many days will half of the original 10 mg of gold-198 remain? e. After how many days will 85% of the gold-198 have decayed? 6. Radioactive decay. Chromium-51 has a decay rate of 2.5% per day. The rate of change of an amount N of chromium-51 after t days is given by dN dt – 0.025N. a. Let No represent the amount of chromium-51 present at i = 0. Find an exponential function that models this situation. b. Suppose 20 mg of chromium-51 is present at 1 = 0. How much will remain after 30 days? c. What is the rate of change of the amount of chromium-51 after 30 days? d. After how many days will half of the original 20 mg of chromium-51 remain? e. After how many days will 95% of the chromium-51 have decayed away? 7. Population decay. Since 1990, the population of Gary, Indiana, has been decreasing by 1.87% per year. The rate of change of the city's population P, t years after 1990, is given by 0.0187P. dt a. In 1990, the population of Gary was 116,646. (Source: U.S. Census Bureau.) Find an exponential function that models this situation. b. Estimate the population of Gary in 2025. c. What is the rate of change of the population of Gary in 2025? d. After how many years will the population of Gary be half of what it was in 1990?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 5T
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7:40 PM Sat Mar 21 * 100%| dN dt 0.2572N. a. Let No represent the amount of gold-198 present at t = 0. Find an exponential function that models this situation. b. Suppose 10 mg of gold-198 is present at 1 = 0. How much will remain after 1 week? c. What is the rate of change of the amount of gold-198 after 1 week? d. After how many days will half of the original 10 mg of gold-198 remain? e. After how many days will 85% of the gold-198 have decayed? 6. Radioactive decay. Chromium-51 has a decay rate of 2.5% per day. The rate of change of an amount N of chromium-51 after t days is given by dN dt – 0.025N. a. Let No represent the amount of chromium-51 present at i = 0. Find an exponential function that models this situation. b. Suppose 20 mg of chromium-51 is present at 1 = 0. How much will remain after 30 days? c. What is the rate of change of the amount of chromium-51 after 30 days? d. After how many days will half of the original 20 mg of chromium-51 remain? e. After how many days will 95% of the chromium-51 have decayed away? 7. Population decay. Since 1990, the population of Gary, Indiana, has been decreasing by 1.87% per year. The rate of change of the city's population P, t years after 1990, is given by 0.0187P. dt a. In 1990, the population of Gary was 116,646. (Source: U.S. Census Bureau.) Find an exponential function that models this situation. b. Estimate the population of Gary in 2025. c. What is the rate of change of the population of Gary in 2025? d. After how many years will the population of Gary be half of what it was in 1990?
Transcribed Image Text:7:40 PM Sat Mar 21 * 100%| dN dt 0.2572N. a. Let No represent the amount of gold-198 present at t = 0. Find an exponential function that models this situation. b. Suppose 10 mg of gold-198 is present at 1 = 0. How much will remain after 1 week? c. What is the rate of change of the amount of gold-198 after 1 week? d. After how many days will half of the original 10 mg of gold-198 remain? e. After how many days will 85% of the gold-198 have decayed? 6. Radioactive decay. Chromium-51 has a decay rate of 2.5% per day. The rate of change of an amount N of chromium-51 after t days is given by dN dt – 0.025N. a. Let No represent the amount of chromium-51 present at i = 0. Find an exponential function that models this situation. b. Suppose 20 mg of chromium-51 is present at 1 = 0. How much will remain after 30 days? c. What is the rate of change of the amount of chromium-51 after 30 days? d. After how many days will half of the original 20 mg of chromium-51 remain? e. After how many days will 95% of the chromium-51 have decayed away? 7. Population decay. Since 1990, the population of Gary, Indiana, has been decreasing by 1.87% per year. The rate of change of the city's population P, t years after 1990, is given by 0.0187P. dt a. In 1990, the population of Gary was 116,646. (Source: U.S. Census Bureau.) Find an exponential function that models this situation. b. Estimate the population of Gary in 2025. c. What is the rate of change of the population of Gary in 2025? d. After how many years will the population of Gary be half of what it was in 1990?
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