A population Model The resident population of the United States in 2014 was 317 million people and was growing at a rate of 0.7% per year. Assuming that this growth continues, the model P ( t ) = 317 ( 1.007 ) t − 2014 represents the population P (in millions of people) in year t . According to this model, when will the population of the United States be 400 million people? According to this model, when will the population of the United States be 435 million people?
A population Model The resident population of the United States in 2014 was 317 million people and was growing at a rate of 0.7% per year. Assuming that this growth continues, the model P ( t ) = 317 ( 1.007 ) t − 2014 represents the population P (in millions of people) in year t . According to this model, when will the population of the United States be 400 million people? According to this model, when will the population of the United States be 435 million people?
A population Model The resident population of the United States in 2014 was 317 million people and was growing at a rate of 0.7% per year. Assuming that this growth continues, the model
P
(
t
)
=
317
(
1.007
)
t
−
2014
represents the population
P
(in millions of people) in year
t
.
According to this model, when will the population of the United States be 400 million people?
According to this model, when will the population of the United States be 435 million people?
3.1 Limits
1. If lim f(x)=-6 and lim f(x)=5, then lim f(x). Explain your choice.
x+3°
x+3*
x+3
(a) Is 5
(c) Does not exist
(b) is 6
(d) is infinite
1 pts
Let F and G be vector fields such that ▼ × F(0, 0, 0) = (0.76, -9.78, 3.29), G(0, 0, 0) = (−3.99, 6.15, 2.94), and
G is irrotational. Then sin(5V (F × G)) at (0, 0, 0) is
Question 1
-0.246
0.072
-0.934
0.478
-0.914
-0.855
0.710
0.262
.
2. Answer the following questions.
(A) [50%] Given the vector field F(x, y, z) = (x²y, e", yz²), verify the differential identity
Vx (VF) V(V •F) - V²F
(B) [50%] Remark. You are confined to use the differential identities.
Let u and v be scalar fields, and F be a vector field given by
F = (Vu) x (Vv)
(i) Show that F is solenoidal (or incompressible).
(ii) Show that
G =
(uvv – vVu)
is a vector potential for F.
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