A Section 4.6 - MATH 19, section 6 x Course Hero X + X C G A webassign.net/web/Student/Assignment-Responses/last?dep=29741500 S GI For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer. Assignment Scoring Your last submission is used for your score. 1. [2/3 Points] DETAILS PREVIOUS ANSWERS SPRECALC7 4.6.001. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This exercise uses the population growth model. A certain culture of the bacterium Streptococcus A initially has 6 bacteria and is observed to double every 1.5 hours. (a) Find an exponential model n(t) = no2 /2 for the number of bacteria in the culture after t hours. n(t) = 6 2 1.5 ) (b) Estimate the number of bacteria after 29 hours. (Round your answer to the nearest whole number.) 15853475 x bacteria (c) After how many hours will the bacteria count reach 10,000? (Round your answer to one decimal place.) t = 16.1 Need Help? Read It Watch It 2. [-/2 Points] DETAILS SPRECALC7 4.6.007.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This exercise uses the population growth model. Oct 17 7:51 1 US 9 0A Section 4.6 - MATH 19, section 6 x Course Hero X + X G G A webassign.net/web/Student/Assignment-Responses/last?dep=29741500 GAO 2. [-/2 Points] DETAILS SPRECALC7 4.6.007.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This exercise uses the population growth model. The population of a country has a relative growth rate of 4% per year. The government is trying to reduce the growth rate to 3%. The population in 2011 was approximately 150 million. Find the projected population for the year 2033 for the following conditions. (Round your answers to the nearest million.) (a) The relative growth rate remains at 4% per year. million people (b) The relative growth rate is reduced to 3% per year. million people Need Help? Read It Watch It Master It 3. [-/2 Points] DETAILS SPRECALC7 4.6.016. MY NOTES ASK YOUR TEACHER This exercise uses the population growth model. The population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year. (a) Estimate how long it takes the population to double. (Round your answer to two decimal places.) yr (b) Estimate how long it takes the population to triple. (Round your answer to two decimal places.) yr Need Help? Read It 9 Oct 17 7:51 1 US 7 0WA Section 4.6 - MATH 19, section 6 X Course Hero X + X webassign.net/web/Student/Assignment-Responses/last?dep=29741500 Q SGAO 4. [-/4 Points] DETAILS SPRECALC7 4.6.018. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This exercise uses the radioactive decay model. The half-life of cesium-137 is 30 years. Suppose we have a 10-g sample. (a) Find a function m(t) = mo2 5/h that models the mass remaining after t years. m(t) = (b) Find a function m(t) = moet that models the mass remaining after t years. (Round your / value to four decimal places.) m(t) = (c) How much of the sample will remain after 74 years? (Round your answer to one decimal place.) (d) After how many years will only 4 g of the sample remain? (Round your answer to the nearest whole number.) yr Need Help? Read It 5. [-/1 Points] DETAILS SPRECALC7 4.6.019. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This exercise uses the radioactive decay model. The half-life of strontium-90 is 28 years. How long will it take a 90-mg sample to decay to a mass of 68.4 mg? (Round your answer to the nearest whole number.) yr Need Help? Read It Watch It Oct 17 7:51 1 US $ 0A Section 4.6 - MATH 19, section 6 x Course Hero X + Lg X G G A webassign.net/web/Student/Assignment-Responses/last?dep=29741500 SGAO 6. [-/1 Points] DETAILS SPRECALC7 4.6.021.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This exercise uses the radioactive decay model. If 250 mg of a radioactive element decays to 200 mg in 36 hours, find the half-life of the element. (Round your answer to the nearest whole number.) hr Need Help? Read It Watch It Master It 7. [-/2 Points] DETAILS SPRECALC7 4.6.022. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This exercise uses the radioactive decay model. After 3 days a sample of radon-222 has decayed to 58% of its original amount. (a) What is the half-life of radon-222? (Round your answer to two decimal places.) days (b) How long will it take the sample to decay to 20% of its original amount? (Round your answer to two decimal places.) days Need Help? Read It 8. [-/1 Points] DETAILS SPRECALC7 4.6.024.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Oct 17 7:51 1 US $ 0A Section 4.6 - MATH 19, section 6 x Course Hero X + Lg X G G A webassign.net/web/Student/Assignment-Responses/last?dep=29741500 SGAO 8. [-/1 Points] DETAILS SPRECALC7 4.6.024.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This exercise uses the radioactive decay model. The burial cloth of an Egyptian mummy is estimated to contain 59% of the carbon-14 it contained originally. How long ago was the mummy buried? (The half-life of carbon-14 is 5730 years. Round your answer to the nearest ten years.) yr Need Help? Read It Master It 9. [-/2 Points] DETAILS SPRECALC7 4.6.026.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This exercise uses Newton's Law of Cooling. Newton's Law of Cooling is used in homicide investigations to determine the time of death. The normal body temperature is 98.6F. Immediately following death, the body begins to cool. It has been determined experimentally that the constant in Newton's Law of Cooling is approximately k = 0.1947, assuming time is measured in hours. Suppose that the temperature of the surroundings is 650F. (a) Find a function 7(t) that models the temperature t hours after death. T ( t ) = (b) If the temperature of the body is now 71F, how long ago was the time of death? (Round your answer to the nearest whole number.) | hr Need Help? Read It Watch It Master It Oct 17 7:51 1 US $ 0VA Section 4.6 - MATH 19, section 6 x Course Hero X + X G G A webassign.net/web/Student/Assignment-Responses/last?dep=29741500 S GI (0 / h the temperature of the boy is now /1 1, how long ago was the time of death? (round your answer to the nearest whole number. ) hr Need Help? Read It Watch It Master It 10. [-/2 Points] DETAILS SPRECALC7 4.6.027.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This exercise uses Newton's Law of Cooling. A roasted turkey is taken from an oven when its temperature has reached 185F and is placed on a table in a room where the temperature is 790F. (a) If the temperature of the turkey is 155F after half an hour, what is its temperature after 45 min? (Round your answer to the nearest whole number.) OF (b) After how many hours will the turkey cool to 100F? (Round your answer to one decimal place.) hr Need Help? Read It Watch It Master It 11. [-/3 Points] DETAILS SPRECALC7 4.6.003. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This exercise uses the population growth model. A grey squirrel population was introduced in a certain county of Great Britain 35 years ago. Biologists observe that the population doubles every 7 years, and now the population is 140,000. (a) What was the initial size of the squirrel population? squirrels wbala Oct 17 7:51 1 US 7 0WA Section 4.6 - MATH 19, section 6 X Course Hero X + X C G A webassign.net/web/Student/Assignment-Responses/last?dep=29741500 Q S 11. [-/3 Points] DETAILS SPRECALC7 4.6.003. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This exercise uses the population growth model. A grey squirrel population was introduced in a certain county of Great Britain 35 years ago. Biologists observe that the population doubles every 7 years, and now the population is 140,000. (a) What was the initial size of the squirrel population? squirrels "b) Estimate the squirrel population 10 years from now. (Round your answer to the nearest whole number.) squirrels (c) Sketch a graph of the squirrel population. (Assume t = 0 corresponds to the initial introduction.) n(t) n(t) 700 000 700 000 600 000 600 000 500 000 500 000 400 000 400 000 300 000 300 000 200 000 200 000 100 000 100 000 t O 10 20 30 40 50 O 10 20 30 40 50 n(t) n(t) 700 000 700 000 9 Oct 17 7:51 1 US 9 0A Section 4.6 - MATH 19, section 6 x *Course Hero X + X G G A webassign.net/web/Student/Assignment-Responses/last?dep=29741500 S GI O 10 20 30 40 50 O 10 20 30 40 50 Need Help? Read It Watch It 12. [-/3 Points] DETAILS SPRECALC7 4.6.013. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This exercise uses the population growth model. A culture starts with 8100 bacteria. After 1 hour the count is 10,000. (a) Find a function that models the number of bacteria n(t) after t hours. (Round your / value to three decimal places.) n(t) = (b) Find the number of bacteria after 2 hours. (Round your answer to the nearest hundred.) bacteria (c) After how many hours will the number of bacteria double? (Round your answer to one decimal place.) hr Need Help? Read It Watch It 13. [-/4 Points] DETAILS SPRECALC7 4.6.017. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This exercise uses the radioactive decay model. Oct 17 7:52 1 US $ 0A Section 4.6 - MATH 19, section 6 x Course Hero X + X G G A webassign.net/web/Student/Assignment-Responses/last?dep=29741500 SGAO 13. [-/4 Points] DETAILS SPRECALC7 4.6.017. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This exercise uses the radioactive decay model. The half-life of radium-226 is 1600 years. Suppose we have a 24-mg sample. (a) Find a function m(t) = mo2-W/ that models the mass remaining after t years. m(t) = (b) Find a function m(t) = moet that models the mass remaining after t years. (Round your / value to six decimal places.) m(t) = (c) How much of the sample will remain after 4500 years? (Round your answer to one decimal place.) mg (d) After how many years will only 16 mg of the sample remain? (Round your answer to one decimal place.) yr Need Help? Read It Watch It 14. [-/1 Points] DETAILS SPRECALC7 4.6.023. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This exercise uses the radioactive decay model. A wooden artifact from an ancient tomb contains 70% of the carbon-14 that is present in living trees. How long ago was the artifact made? (The half-life of carbon-14 is 5730 years. Round your decay rate, r, to 6 decimal places. Then round your answer to the nearest whole number.) yr Oct 17 7:52 1 US $ 0