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.]
Exer. 31-32: Find an exponential function of the form
f(x) = ba-* + c that has the given horizontal asymptote and
y-intercept and passes through point P.
31 y = 32; y-intercept 212; P(2, 112)
32 y = 72; y-intercept 425; P(1, 248.5)
Births to Unmarried Mothers The percent of livebirths to unmarried mothers for the years 1970–2007can be modeled by the logistic functiony = 44.742/1 + 6.870e-0.0782xwhere x is the number of years after 1960.a. Use this model to estimate the percent in 1990 andin 1996.b. What is the upper limit of the percent of teenmothers who were unmarried, according to thismodel?
Consumer expenditures, in millions of dollars, on all types of books in the United States for the years 1995-2005 can be modeled by the function defined by
B(x) = 25,280 e0.0425x where x- 0 represents 1995, x 1 represents 1996, and so on. Approximate consumer expenditures for 2003.
The total expenditures in the year 2003 was approximately million dollars.
(Round to the nearest integer as needed.)
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