1. Carbon-14 is used to determine the age of artifacts in carbon dating. Carbon-14 has a half-life of 5730 years. Write an expon
ential decay function for a 52-mg sample
1 answer:
See the attached graphic. (I'm rewording the attached formula)
Ending amount = Beginning Amount * e ^(k * t)
where "e" is the mathematical constant 2.718281828
and k = natural log (.5) / half-life
k = -.693147 / 5,730 = <span><span><span>-0.000120968062827225 </span> </span> </span>
Ending amount = 52 * e ^(-0.000120968062827225* t)
As a test, let's see how much remains after <span> <span> <span> 11,460 </span> years.</span>
</span>Ending amount = 52 * e ^(-0.000120968062827225 * 11,460)
Ending amount = 52 * e ^ ( <span> <span> <span> -1.386294 </span> </span> </span> )
Ending amount = 52 * <span> <span> <span> 0.250000
</span></span></span>Ending amount = 13
(which is correct because that is one quarter of the amount after two half-lives).
Source:
http://www.1728.org/halflif2.htm
Ending amount = Beginning Amount * e ^(k * t)
where "e" is the mathematical constant 2.718281828
and k = natural log (.5) / half-life
k = -.693147 / 5,730 = <span><span><span>-0.000120968062827225 </span> </span> </span>
Ending amount = 52 * e ^(-0.000120968062827225* t)
As a test, let's see how much remains after <span> <span> <span> 11,460 </span> years.</span>
</span>Ending amount = 52 * e ^(-0.000120968062827225 * 11,460)
Ending amount = 52 * e ^ ( <span> <span> <span> -1.386294 </span> </span> </span> )
Ending amount = 52 * <span> <span> <span> 0.250000
</span></span></span>Ending amount = 13
(which is correct because that is one quarter of the amount after two half-lives).
Source:
http://www.1728.org/halflif2.htm
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Answer:
The first option
Step-by-step explanation:
Given a quadratic function in standard form : ax² + bx + c : a ≠ 0, then
The equation of the axis of symmetry which is also the x- coordinate of the vertex is found using
x = -
f(x) = - 2x² - 2x - 1 ← is in standard form
with a = - 2, b = - 2, so
x = - = - 0.5
Equation of axis of symmetry is x = - 0.5
Substitute x = - 0.5 into f(x)
f(- 0.5) = - 2(- 0.5)² - 2(- 0.5) - 1 = - 0.5 + 1 - 1 = - 0.5
Vertex = (- 0.5, - 0.5 )