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#2016Exams
100
e^(-3x)=5
x=ln(5)/-3 or approx. x=-0.5365
100
Find the simple interest earned on a loan for $8,000 at 6.3% for 72 days.
$99.42
100
Write the equation of the line that goes through the point (1,3) and has slope 2 in slope-intercept form.
y=2x+1
100
Find a linear cost function given: Fixed cost: $200, 50 items cost $2,000 to produce
C(x)= 36x +200
100
Find the equation of a line through (1/3, 0) and parallel to the line 6x-2y=11.
y=3x-1
200
3*ln(3x-1)=12
x=(e^4 + 1)/3 or approx. x = 18.5327
200
Find the simple interest earned on $2000 invested at 17% over 4 years.
$1360.
200
Use the data to find a linear model: Year: 5 , 7, Number of faculty: 917 , 991
y=37x+732
200
Given R(x)=125x and C(x)=100x+5000. Suppose x is the number of tv's sold. Find the number of tv's you need to sell to break-even.
x=200 t.v's
200
How long will it take $1,000 to grow to $3600 if it is invested at 4% compounded quarterly?
About 32 years.
300
Log (base 2) (x)+ Log (base 2) (x+2)=3
x=2 (-4 is not in domain)
300
A newborn child receives a $20,000 gift toward college from her grandparents. How much will the $20,000 be worth in 18 years if it is invested at 10% compounded continuously?
$120,992.95
300

Find the vertex and x & y intercepts of the function f(x)= 15x^2+23x-28

y-intercept: -28

x-intercepts: -7/3 and 4/5

vertex: (-23/30, -2209/60)

300

Suppose the revenue for Bulldog bus company depends on the number of unsold seats. Let s(x) represent the number of sold seats, and p(x) the price per seat. Given s(x)=100-x, and p(x)=50+x, find the maximum revenue.

R(x)=s(x)*p(x)=-x^2 +50x +5000 x=25 produces the max revenue. max revenue= $5625

300
Suppose the balance on your credit card is modeled by B(t)=1500(0.9604)^t. a) What was your initial balance on the card? b) What type of model is this? c) Will you ever pay off the card?
a) $1500 b) exponential decay c) Nope. B(t)>0 for all t>0.
400
5^(x^2+x)=1
x=0, -1
400
How long will it take money to quadruple if it is invested at 6% compounded annually?
23.79 years
400
What is the domain of f(x)=log(0.5-3x)
x<(1/6)
400
Suppose you have the following data on death rates per 100,000 Americans: Year: 2000 , 2010, Rate: 257.6 , 178.5 Fit an exponential model and use it to estimate the death rates in the year 2012.
Model: f(t)=257.6(.964)^t Death rate in 2012 --> f(12)=165.9
400
A producer estimates that it will cost $70,000 to shoot a marketing tape for college education. It will cost $15 to copy and distribute the tape to clients. Clients pay $50 to use the tape for their marketing purposes. How many tapes must the producer sell to break-even?
P(x)=35x-70,000 Break even: x=2000 tapes.
500
3^(2x)=4^(x+1)
x= ln(4)/(2ln(3)-ln(4)) or approx x=1.7095
500
Your faculty retirement plan is an annuity with a guaranteed return of 7% per year (compounded monthly). You want $800,000 when you retire in 50 years. How much money will you need to deposit each month to reach your goal?
$146.84
500
Find the domain of the function: f(x)= sqrt(x)/(x^2 -3x +2)
[0, 1) U (1, 2) U (2, infinity)
500
You manage a pop machine and are willing to stock 300 cans per week when the price is $.50/can and 500 cans per week when the price is $.75 per can. If demand can be modeled with q=-200p+500, find the equilibrium price.
Supply equation: q=800p-100. Equilibrium Price: $0.60 per can.
500
A standard repayment plan on a student loan is equal monthly payments for 10 years. If a student borrows $35,000 at 7.43% interest, find the monthly payment and total interest paid under the plan.
R= $414.18 Interest Paid: $14, 701.60