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A curve passes through the point (0, 2) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve? (Use x as the independent variable y(x) =

A curve passes through the point (0, 2) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve? (Use x as the independent variable y(x) =

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section1.3: Lines
Problem 1E
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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, **C, with a half-life 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 often dated by using an element other than carbon, like potassium-40, that has a longer half-life (in this case, approximately 1.25 billion years). Suppose the minimum detectable mass is 0.4% and a dinosaur is dated with 40K to be 66 million years old. Is such a dating possible? Yes, it is possible to date this fossil with 40K. O No, it is not possible to date this fossil with 40K. What is the maximum age (in millions of years) of a fossil that could be dated using 40K? (Round your answer to one decimal place.) 3188.13 x million years
Transcribed Image Text: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, **C, with a half-life 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 often dated by using an element other than carbon, like potassium-40, that has a longer half-life (in this case, approximately 1.25 billion years). Suppose the minimum detectable mass is 0.4% and a dinosaur is dated with 40K to be 66 million years old. Is such a dating possible? Yes, it is possible to date this fossil with 40K. O No, it is not possible to date this fossil with 40K. What is the maximum age (in millions of years) of a fossil that could be dated using 40K? (Round your answer to one decimal place.) 3188.13 x million years
A curve passes through the point (0, 2) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve? (Use x as the independent variable.) y(x) =
Transcribed Image Text:A curve passes through the point (0, 2) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve? (Use x as the independent variable.) y(x) =
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