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Posted: April 9th, 2022

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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