17. [-/5 Points] DETAILS SCALCET9 3.XP.8.001. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 75 cells. (a) Find the relative growth rate. (Assume t is measured in hours.) K = (b) Find an expression for the number of cells after t hours. P (t) = (c) Find the number of cells after 8 hours. cells (d) Find the rate of growth after 8 hours. (Round your answer to three decimal places.) billion cells per hour (e) When (in hours) will the population reach 20,000 cells? (Round your answer to two decimal places.) h Need Help? Read It16. [0/2 Points] DETAILS PREVIOUS ANSWERS SCALCET9 3.8.017. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER When a cold drink is taken from a refrigerator, its temperature is 5C. After 25 minutes in a 20C room its temperature has increased to 10C. (Round your answers to two decimal places.) (a) What is the temperature of the drink (in C) after 45 minutes? 11.50 X C (b) After how many minutes will its temperature reach 16.C? 81.49 X min Need Help? Read It Watch It13. [12 Points] - SCALCETQ 3.8.012. ASK YOUR TEACHER PRACTICE ANOTHER Scientists can determine the age of ancient objects by the method of radiocarbon dating. The bombardment of the upper atmosphere by cosmic rays converts nitrogen to a radioactive isotope of carbon, MCI with a halfelife of about 5,730 years. Vegetation absorbs carbon dioxide through the atmosphere, and animal life aSSimilates 14C through food chains. When a plant or animal dies, it stops replacing its carbon, and the amount of 14C present begins to decrease through radioactive decay. Therefore, the level of radioactiVity must also decay exponentially. Dinosaur fossils are too old to be reliably dated using carbonel4. Suppose we had a 66 million year old dinosaur fossil. What percent of the living dinosaur's 14C would be remaining today? (Round your answer to five decimal places.) E % Suppose the minimum detectable amount is 0.5%. What is the maximum age [in years) of a fossil that we could date using 14C? (Round your answer to the nearest year.) :vr Need Help? PREVIOUS ANSWERS SCALCET9 3.8.015.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A roast turkey is removed from an oven when its temperature has reached 185F and is placed on a table in a room where the ambient temperature is 75'1F. (Round your answers to the nearest whole number.) 14. [0/1 Points] (a) If the temperature of the turkey is 150F after half an hour, what is the temperature (in DF) after 40 minutes? W :x .F (b) After how many minutes will the turkey have cooled to 90F? NeenHemv 11. [0/4 Points] DETAILS PREVIOUS ANSWERS SCALCET9 3.8.003. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A culture of the bacterium Salmonella enteritidis initially contains 50 cells. When introduced into a nutrient broth, the culture grows at a rate proportional to its size. After 1.5 hours, the population has increased to 825. (a) Find an expression for the number of bacteria after t hours. (Round your numeric values to four decimal places.) P(t) = 50 (11 ) X (b) Find the number of bacteria after 5 hours. (Round your answer to the nearest whole number.) P(5) = 8052550 x bacteria (c) Find the rate of growth (in bacteria per hour) after 5 hours. (Round your answer to the nearest whole number.) P'(5)= 19309172 x bacteria per hour (d) After how many hours will the population reach 250,000? (Round your answer to one decimal place.) t = 3.6 X hr Enhanced Feedback Please try again. Recall that a bacteria culture with growth rate proportional to the size of the culture has a growth function in the form of P(t) = P(0)ekt, where P(0) is the initial value and k is the growth rate. Find k by replacing other values in the equation with given values from the problem. Need Help? Read It Watch It10. [-/5 Points] DETAILS SCALCET9 3.8.002. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A common inhabitant of human intestines is the bacterium Escherichia coli, named after the German pediatrician Theodor Escherich, who identified it in 1885. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 50 cells. (a) Find the relative growth rate. K = hr- 1 (b) Find an expression for the number of cells after t hours. P(t) = (c) Find the number of cells after 8 hours. cells (d) Find the rate of growth after 8 hours. (Round your answer to the nearest integer.) cells/h (e) When will the population reach a million cells? (Round your answer to two decimal places.) h Need Help? Read It Submit AnswerNewton's Law ot Gravitation says that the magnitude F of the torce exerted by a body ot mass m on a body ot mass M is G M F = m I r2 where G is t1e gravitational constant and r is the distance between the bodies. . dF a Find . ( ) o'r E : dr What is the meaning of $ in the context of this probiem? r Q % represents the rate of change of the force with respect to the distance between the bodies. ,, C- ? represents the rate of change of the mass with respect to the distance between the bodies. r C- ? represents the rate of change of the distance between the bodies with respect to the force. r % represents the amount of force per distance. ,, Q % represents the rate of change of the mass with respect to the force. ,, What does the minus sign in the expression indicate? (3- The minus sign indicates that as the distance between the bodies increases, the magnitude of the force decreases. C- The minus sign indicates that the force between the bodies is decreasmg. CO) The minus sign indicates that the bodies are being towed in the negative direction. The minus sign indicates that as the distance between the bodies decreases] the magnitude of the force remains constant. V The minus sign indicates that as the distance between the bodies increases, the magnitude of the force increases. (b) Suppose it is known that the earth attracts an object with a force that decreases at the rate of 2 N/km when r : 30,000 km. How fast does this force change when r : 15.000 km? E m