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.]
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
2. Find a matrix A with the following qualities
a. A is 3 x 3.
b. The matrix A is not lower triangular and is not upper triangular.
c. At least one value in each row is not a 1, 2,-1, -2, or 0
d. A is invertible.
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