The half-life of radium-226 is 1620 yr. Given a sample of 1 g of radium-226, the quantity left Q t (in g) after t years is given by Q t = 1 2 t / 1620 . a. Convert this to an exponential function using base e . b. Verify that the original function and the result from part (a) yield the same result for Q 0 , Q 1620 , and Q 3240 . (Note: There may be round-off error.)
The half-life of radium-226 is 1620 yr. Given a sample of 1 g of radium-226, the quantity left Q t (in g) after t years is given by Q t = 1 2 t / 1620 . a. Convert this to an exponential function using base e . b. Verify that the original function and the result from part (a) yield the same result for Q 0 , Q 1620 , and Q 3240 . (Note: There may be round-off error.)
The half-life of radium-226 is 1620 yr. Given a sample of 1 g of radium-226, the quantity left
Q
t
(in g) after t years is given by
Q
t
=
1
2
t
/
1620
.
a. Convert this to an exponential function using base e.
b. Verify that the original function and the result from part (a) yield the same result for
Q
0
,
Q
1620
,
and
Q
3240
.
(Note: There may be round-off error.)
2. (5 points) Let f(x) =
=
-
-
- x² − 3x+7. Find the local minimum and maximum point(s)
of f(x), and write them in the form (a, b), specifying whether each point is a minimum
or maximum. Coordinates should be kept in fractions.
Additionally, provide in your answer if f(x) has an absolute minimum or maximum
over its entire domain with their corresponding values. Otherwise, state that there is no
absolute maximum or minimum. As a reminder, ∞ and -∞ are not considered absolute
maxima and minima respectively.
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