Doctorates in Mexico The annual number of PhD graduates in Mexico in the natural sciences for 1990–2012 can be approximated by n ( t ) = 890 ( 1 − e − 0.05 t ) , where t is time in years since 1990. 2 Numerically estimate lim x → + ∞ n ( t ) , and interpret the answer. [ HINT: See Example 6.]
Doctorates in Mexico The annual number of PhD graduates in Mexico in the natural sciences for 1990–2012 can be approximated by n ( t ) = 890 ( 1 − e − 0.05 t ) , where t is time in years since 1990. 2 Numerically estimate lim x → + ∞ n ( t ) , and interpret the answer. [ HINT: See Example 6.]
Solution Summary: The author analyzes the function n(t)=890(1-e-0.05t), where t is the time in years since 1990, and interprets that there will
Doctorates in Mexico The annual number of PhD graduates in Mexico in the natural sciences for 1990–2012 can be approximated by
n
(
t
)
=
890
(
1
−
e
−
0.05
t
)
,
where t is time in years since 1990.2 Numerically estimate
lim
x
→
+
∞
n
(
t
)
,
and interpret the answer. [HINT: See Example 6.]
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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