Question

1. Find the rate of change of *y* with respect to
*x* at the indicated value of *x*. y =

x tan(x) |

3 sec(x) |

; x = 0

y' = _____

2. The total world population is forecast to be

P(t) = 0.00066t^{3} − 0.0713t^{2} + 0.84t +
6.04 (0 ≤ t ≤ 10) in year *t*, where
*t* is measured in decades, with *t* = 0
corresponding to 2000 and *P*(*t*) is measured in
billions.

(a) World population is forecast to peak in what year?
**Hint:** Use the quadratic formula. (Remember that
*t* is in decades and not in years. Round your answer down
to the nearest year.)

____________

(b) At what number will the population peak? (Be sure to use the
value of *t* found in part (a). Round your answer to two
decimal places.)

____________ billion

Answer #1

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1.
The total world population is forecast to be
P(t) = 0.00073t3 − 0.072t2 + 0.9t +
6.04 (0 ≤ t ≤ 10)
in year t, where t is measured in decades,
with t = 0 corresponding to 2000 and
P(t) is measured in billions.
a. World population is forecast to peak in what year?
Hint: Use the quadratic formula. (Remember that
t is in decades and not in years. Round your answer down
to the nearest year.)
________
b. At...

The population of the world was about 5.3 billion in 1990 (t =
0) and about 6.1 billion in 2000 (t = 10). Assuming that the
carrying capacity for the world population is 50 billion, the
logistic differential equation
dP =kP(50−P)dt
models the population of the world P(t) (measured in billions),
where t is the number of years after 1990. Solve this differential
equation for P(t) and use this solution to predict what the
population will be in 2050 according...

1. Find a function f given that the slope of the tangent line to
the graph of f at any point P(x, y) is given by y' = − 4xy x2 + 1
and the graph of f passes through the point (2, 1).
2. The world population at the beginning of 1980 (t =
0) was 4.5 billion. Assuming that the population continued to grow
at the rate of approximately 2%/year, find a function
Q(t) that expresses the world...

. Find a cubic function f(x) with roots x = 4, x = 1, x = −2 and
f(1) = 16.
3. Sketch the graph of f(x) = (x − 2)/x^2−3x−4 showing zeros,
intercepts, and asymptotes.
4. Assume that world population(in billions of people) in t
years since 2016 is given by y = 7.7e^0.01t . When will the
population reach 9 billion?
5. Solve for x: log3 (x + 2) + log3 (x − 4) = 3.
6. Show...

1) Find the values of the trigonometric functions of θ from the
information given.
cot(θ) = − 3/5, cos(θ) > 0
sin(θ)
=
cos(θ)
=
tan(θ)
=
csc(θ)
=
sec(θ)
=
2)
The point P is on the unit circle. Find
P(x, y) from the given information.
The x-coordinate of P is −√5/4, and P
lies below the x-axis.
P(x, y) = ( )
3) Find the terminal point P(x, y) on the unit circle
determined by the given value of...

Find the general solution and initial value solution: (cos x)dy
= -2y2(tan x)dx, y(0)=1/6

For each vector field F~ (x, y) = hP(x, y), Q(x, y)i, find a
function f(x, y) such that F~ (x, y) = ∇f(x, y) = h ∂f ∂x , ∂f ∂y i
by integrating P and Q with respect to the appropriate variables
and combining answers. Then use that potential function to directly
calculate the given line integral (via the Fundamental Theorem of
Line Integrals):
a) F~ 1(x, y) = hx 2 , y2 i Z C F~ 1...

1) x = t^3 + 1 , y = t^2 - t , Find an equation of the tangent
to the curve at the point corresponding to t = 1
2) x = t^2 + 1 , y = 3t^2 + t ,Find
a) dy/dx ,
b) (d^2)y / dx^2
c) For which values of t is the curve concave upward?
3) sketch the curve: r = 1 - 3cos θ
4)A demand curve is given by p = 450/(x...

Find the average value of f(x, y) = 1/x over the circle in R2 of
radius 1 centered at (1,0). (Hint: use polar coordinates; remember
you already know a formula for the area of a circle).

The population P (in thousands) of a certain city from 2000
through 2014 can be modeled by P = 160.3e ^kt, where t represents
the year, with t = 0 corresponding to 2000. In 2007, the population
of the city was about 164,075.
(a) Find the value of k. (Round your answer to four decimal
places.)
K=___________
Is the population increasing or decreasing? Explain.
(b) Use the model to predict the populations of the city (in
thousands) in 2020 and...

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