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Concept explainers
A researcher is trying to determine the doubling time for a population of the bacterium Giardia lamblia. He starts a culture in a nutrient solution and estimates the bacteria count every four hours. His data are shown in the table.
Time (hours) | 0 | 4 | 8 | 12 | 16 | 20 | 24 |
Bacteria count (CFU/mL | 37 | 47 | 63 | 78 | 105 | 130 | 173 |
(a) Make a
(b) Use a graphing calculator to find an exponential curve
(c) Graph the model from part (b) together with the scatter plot in part (a) Use the TRACE feature to determine how long it takes for the bacteria count to double.
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Chapter 6 Solutions
Calculus (MindTap Course List)
- Decide whether each limit exists. If a limit exists, estimate its value. 11. (a) lim f(x) x-3 f(x) ↑ 4 3- 2+ (b) lim f(x) x―0 -2 0 X 1234arrow_forwardDetermine whether the lines L₁ (t) = (-2,3, −1)t + (0,2,-3) and L2 p(s) = (2, −3, 1)s + (-10, 17, -8) intersect. If they do, find the point of intersection.arrow_forwardConvert the line given by the parametric equations y(t) Enter the symmetric equations in alphabetic order. (x(t) = -4+6t = 3-t (z(t) = 5-7t to symmetric equations.arrow_forward
- Find the point at which the line (t) = (4, -5,-4)+t(-2, -1,5) intersects the xy plane.arrow_forwardFind the distance from the point (-9, -3, 0) to the line ä(t) = (−4, 1, −1)t + (0, 1, −3) .arrow_forward1 Find a vector parallel to the line defined by the parametric equations (x(t) = -2t y(t) == 1- 9t z(t) = -1-t Additionally, find a point on the line.arrow_forward
- Find the (perpendicular) distance from the line given by the parametric equations (x(t) = 5+9t y(t) = 7t = 2-9t z(t) to the point (-1, 1, −3).arrow_forwardLet ä(t) = (3,-2,-5)t + (7,−1, 2) and (u) = (5,0, 3)u + (−3,−9,3). Find the acute angle (in degrees) between the lines:arrow_forwardA tank initially contains 50 gal of pure water. Brine containing 3 lb of salt per gallon enters the tank at 2 gal/min, and the (perfectly mixed) solution leaves the tank at 3 gal/min. Thus, the tank is empty after exactly 50 min. (a) Find the amount of salt in the tank after t minutes. (b) What is the maximum amount of salt ever in the tank?arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
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