The bones of a newly discovered dinosaur weigh 170 pounds and measure 9 feet, with a 6-inch claw on one toe of each hind foot The age of the dinosaur was estimated using a radioactive substance dating of rocks surrounding the bones. Complete parts a and b. a. The radioactive substance decays exponentially with a half-life of approximately 1.22 billion years. Use the fact that after 1.22 billion years a given amount of the radioactive substance will have decayed to half the original amount to show that the decay model for the radioactive substance is given by A = An e -0 56815t where t is in billions of years. oe To show that the decay model for the radioactive substance is A= An e-0 56815t find the decay rate k for a substance, Substitute the values of A and t in the exponential decay model, A= A, e A=A, ek Ag = A, e122k 2 Substitute D=e1.22k Divide both sides of the equation by Ag-
The bones of a newly discovered dinosaur weigh 170 pounds and measure 9 feet, with a 6-inch claw on one toe of each hind foot The age of the dinosaur was estimated using a radioactive substance dating of rocks surrounding the bones. Complete parts a and b. a. The radioactive substance decays exponentially with a half-life of approximately 1.22 billion years. Use the fact that after 1.22 billion years a given amount of the radioactive substance will have decayed to half the original amount to show that the decay model for the radioactive substance is given by A = An e -0 56815t where t is in billions of years. oe To show that the decay model for the radioactive substance is A= An e-0 56815t find the decay rate k for a substance, Substitute the values of A and t in the exponential decay model, A= A, e A=A, ek Ag = A, e122k 2 Substitute D=e1.22k Divide both sides of the equation by Ag-
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 62SE: A scientist begins with 100 milligrams of aradioactive substance that decays exponentially. After 35...
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4.5-11
Transcribed Image Text:The bones of a newly discovered dinosaur weigh 170 pounds and measure 9 feet, with a 6-inch claw on one toe of each hind foot. The age of the dinosaur was estimated using a radioactive substance dating
of rocks surrounding the bones.
Complete parts a and b.
a. The radioactive substance decays exponentially with a half-life of approximately 1.22 billion years. Use the fact that after 1.22 billion years a given amount of the radioactive substance will have decayed to
half the original amount to show that the decay model for the radioactive substance is given by A = An e -0.56815t where t is in billions of years.
To show that the decay model for the radioactive substance is A= An e-0 56815t find the decay rate k for a substance. Substitute the values of A and t in the exponential decay model, A= A, e".
A=A, ekt
Ap
= Ag e1 22k
2
Substitute
Divide both sides of the equation by Ag-
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