Posted: April 9th, 2022

Math

1. On condition that y = 1.6
−x
, write an equal equation within the kind y = b
x
, with zero < b < 1
y=_____________
2. If $1200 is invested for x years at eight%, compounded quarterly, the long run worth that
will result’s represented by the next equation.
S = 1200(1.02)
4x
What quantity will lead to four years? (Spherical your reply to the closest cent.)
$______________
three. The buying energy P of a set earnings of $20,000 per 12 months (corresponding to a pension)
after t years of seven% inflation could be modeled by
P = 20,000(1.07)
−t
.
(a) Discover the buying energy after 5 years. (Spherical your reply to the closest
greenback.)
$_______________
(b)Discover the buying energy after 20 years. (Spherical your reply to the closest
greenback.)
$________________
four. If $1000 is invested for x years at 10%, compounded repeatedly, the long run worth
that outcomes is
S = 1000e
zero.10x
.
What quantity will lead to three years? (Spherical your reply to the closest cent.)
$______________
5. Clear up the equation.
log(x) = 6
x=__________
6. Clear up for x by writing the equation in exponential kind.
log(3x − four) = 2
x=______________
7. Clear up for x by writing the equation in exponential kind. (Spherical your reply to 3
decimal locations.)
ln(2x + four) = 2.three
x=_____________
eight. Write the equation in logarithmic kind and resolve for x. (Spherical your reply to 3
decimal locations.)
e
9x + 5 = zero.51
x=____________
9. Clear up the equation. Give your reply appropriate to three decimal locations.
95,000 = 10,000(1.02)
3x
x = ____________
10.Clear up the equation. Give your reply appropriate to three decimal locations.
10,000 = 1500e
zero.07x
x = _____________
11.Clear up the equation. Give your reply appropriate to three decimal locations.
82 = 100 − 100e
−zero.07x
x = _____________
12. The gross sales decay for a product is given by S = 80,000e
−zero.5x
, the place S is the month-to-month
gross sales and x is the variety of months which have handed for the reason that finish of a promotional
marketing campaign.
(a)What would be the gross sales 6 months after the tip of the marketing campaign? (Spherical your
reply to 2 decimal locations.)
$______________
(b)What number of months after the tip of the marketing campaign will gross sales drop under $1,000, if
no new marketing campaign is initiated? (Spherical as much as the closest complete quantity.)
_____________months
13. For the years from 2002 and projected to 2024, the nationwide well being care
expenditures H, in billions of dollars, could be modeled by
H = 1,500e
zero.053t
the place t is the variety of years previous 2000.† In what 12 months are nationwide well being care
expenditures anticipated to succeed in $four.zero trillion (that’s, $four,000 billion)?
_______________
14. Disposable earnings is the quantity out there for spending and saving after taxes have
been paid and is one gauge for the state of the economic system. Utilizing U.S. Power
Administration knowledge for chosen years from 2010 and projected to 2040, the entire
U.S. disposable earnings, in billions, could be modeled by
D(t) = 10,zero20e
zero.02292t
the place t is the variety of years previous 2010. In what 12 months is disposable earnings
predicted to be $15 trillion (that’s, $15,000 billion)?
________________
15. The demand operate for a sure commodity is given by p = 100e
−q/2
. (p is the worth
per unit and q is the variety of models.)
(a)At what value per unit will the amount demanded equal 6 models? (Spherical your
reply to the closest cent.)
$_______________
(b)If the worth is $1.79 per unit, what number of models might be demanded, to the closest
unit?
_______________units
16. The overall value operate for a product is C(x) = 650 ln(x + 10) + 1700
the place x is the variety of models produced.
(a) Discover the entire value of manufacturing 100 models. (Spherical your reply to the closest
cent.)
$__________________
(b)Producing what number of models will give whole prices of $7500? (Spherical your reply to
the closest complete quantity.)
______________units
17.Suppose the provision of x models of a sure product at value p dollars per unit is given
by p = 16 + 6 ln(2x + 1).
What number of models of this product can be provided when the worth is $52 every?
(Spherical your reply to the closest complete quantity.)
______________units

————

1. Assume y = 1.6 x.

, assemble an identical equation of the shape y = b

x

, the place zero b 1

y=_____________

2. If $1200 is invested for x years at eight% compounded quarterly, what’s the future worth?

The next equation represents the tip end result.

1200 = S (1.02)

4x

What quantity will lead to four years? (Spherical your reply to the closest cent.)

$______________

three. The buying energy P of a set earnings of $20,000 per 12 months (corresponding to a pension)

after t years of seven% inflation could be modeled by

P = 20,000(1.07)

−t

.

(a) Discover the buying energy after 5 years. (Spherical your reply to the closest

greenback.)

$_______________

(b)Discover the buying energy after 20 years. (Spherical your reply to the closest

greenback.)

$________________

four

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