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.]
Given lim (4x-3) as x approaches 1.
Use the definition of a limt to find a number delta such that the absolute value of x-a is less than delta when the absolute value of f(x)-L is less than 0.08
Movie expenditures, in billions of dollars, on advertising in a certain format from 1995 to 2004 can be approximated by
f(t) =
0.04t + 0.33
if t ≤ 4
−0.01t + 1.5
if t > 4,
where t is time in years since 1995.
(a)
Compute
lim t→4− f(t).
(If an answer does not exist, enter DNE.)
Interpret the answer.
Shortly 1999 (t = 4), annual advertising expenditures were close to $ billion.
Compute
lim t→4+ f(t).
(If an answer does not exist, enter DNE.)
Interpret the answer.
Shortly 1999 (t = 4), annual advertising expenditures were close to $ billion.
(b)
Is the function f continuous at t = 4?
YesNo
What does the answer tell you about movie advertising expenditures?
Movie advertising expenditures in 1999.
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