Expert: Richard J. Raridon - 4/8/2008

Question
Use Descarte's Rule 0f Signs to determine the possible number of positive and negative real zeros for the given function: f(x)=8x^4-5x^3+x^2-4x+10

Possible answers:
4 positive zeros; no negative zeros
4,2 or 0 positive zeros, no negative zeros
4,2 or 0 positive zeros, 1 negative zeros
4 or 2 positive zeros, no negative zeros (the one I chose)

Along with incomes, people's charitable contributions have steadily increased over the past few years.  The table below shows the average deduction for charitable contributions reported on individual income tax returns for the period 1993 to 1998.  Find the average annual increase between 1995 and 1997.

Year   Charitable Contributions
1993     $1800
1994     $2400
1995     $2480
1996     $2810
1997     $3030
1998     $3170

Solve the problem:
A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground.  696 feet of fencing is used.  Find the maximum area of the playground.

Possible answers:
22,707 ft^2
30,276 ft^2
15,138 ft^2
20,184 ft^2

Solve the problem:
The rational function: C(x)=140x/100-x, 0<x<100 describes the cost, C, in millions of dollars, to innoculate x% of the population against a particular strain of the flu.  Determine the difference in cost between innoculating 65% of the population and innoculating 35% of the population.  (Round to the nearest tenth, if necessary).

Possible answers:
$1.8 millin
$184.6 miilion
$184.7 million
$1.9 miilion

A ball is thrown vertically upward with an initial velocity of 160 feet per second.  The distance in feet of the ball from the ground after t seconds is s=160t-16t^2.  For what intervals of time is the ball less than 336 above the ground (after it is tossed until it returns to the ground).

Possible answers:
between 0 and 3 seconds and between 7 and 10 seconds
between 0 and 2.5 seconds and between 7.5 and 10 seconds
between 0 and 4.5 seconds and between 5.5 and 10 seconds
between 3 and 7 seconds (this is the one I chose)

Find functions f and g so that h(x)=(f*g)(x)

h(x)=(-5x-12)7

Possible answers:

f(x)=-5x-12, g(x)=x7 (I chose this answer)
f(x)=(-5x)7, g(x)=-12
f(x)=x7, g(x)=-5x-12
f(x)=-5x7, g(x)=x-12

Use synthetic division to show that the number given to the right of the equation is a solution of the equation, and then solve the polynomila equation.

4x^3+24x^2+12x-40=0;-2

Possible answers:
{-5/4,4,-2}
{-1,-5,-2}
{1,-5,-2}
{1,5,-2} (I chose this answer)

Use the compound interest formulas A=P(1+r/n)nt and A=pert to solve.

Suppose you have $9000 to invest.  Which investment yields the greater return over 5 years: 6.25% compunded continuously or 6.3% compounded semiannually?

Possible answers:

$9000 invested at 6.3% compounded semiannually over 5 years yields the greater return.  (I chose this answer, but I believe it is the third)

Both investment plans yield the same return.

$9000 invested at 6.25% compounded continuously over 5 years yields the greater retrun.

Can you show me how to solve these problems?  I ama little confused...I was never good at word problems... I think I may read too much into the problem and confuse myself.. I appreciate any assistance you can provide me with.

V/R

Nicole

Answer
1) there are no real zeros
2) 95-96 13.3%, 96-97 7.8%, average 10.6%
3) 20,184 ft^2
4) 184.6
5) Obviously, at zero time, it's below 336, between 3 and 7 is the time it's above 336.
6) none of these answers are correct if you wrote h(x) correctly.
7) (1,-5,-2)
8) In one case, r = 0.063, n=2, t=5
In the other case, r= 0.0625, n=365, t=5, third answer is correct.