Pre - Calculus Part 1: Lesson 3 and Lesson 4 Quizzes
A corporate jet originally cost $17,550,000. If its value depreciates by 5 percent per year, what will its value be after 10 years?
$10,507,833.28
The nationwide average salary of a computer programmer can be modeled by the equation , where y is the salary in thousands of dollars and n is the number of years since 1990.Graph the function. Then, using this model, predict the average programmer's salary in 2010.
$102,000
If the Laffite family deposits $8500 in a savings account at 6.75% interest, compounded continuously, how much will be in the account after 25 years?
$45,950.57
Jimmy invests $500 in an account with a 3% interest rate, making no other deposits or withdrawals. What will Jimmy's account balance be after 10 years if the interest is compounded 2 times each year?
$673.43
Use the end behavior of the graph to solve 3x^3 + 9x^2 - 12x < 0
(- ∞, -4) or (0, 1)
Use a sign chart to solve (2x + 3)(x + 8) ≥ 0.
(-∞, -8] or [-3/2, ∞)
Determine which consecutive integers do not have a real zero of f(x) = x^3 + 9x^2 + 8x - 5 between them.
(4, 5)
Factor x^3 - 3x^2 - 4x + 12 completely using long division if (x - 2) is a factor.
(x - 2)(x + 2)(x - 3)
Solve e^-5x = 7.4 for x correct to four decimal places.
-0.4003
Solve. ln(-x + 1) - ln(3x + 5) = ln(-6x + 1)
-1.58 or 0.14 (you can use mathway too)
Evaluate the expression logv5 1/25.
-2
Solve each inequality. Round to the nearest hundredth. 3x^2 - 4 ≤ 6 - 5x
-2.84 ≤ x ≤ 1.17
Solve each equation. 4/x-4 - 7/x+5 = 66/x^2 + x - 20
-6 (you can use mathway as well)
Divide (28x^5 + 29x^4 + 5x^3 + 86x^2 + 56x + 53) by (-4x - 7) using synthetic division.
-7x4 + 5x3 - 10x2 - 4x - 7 + 4/-4x-7
Solve. x-7/x-4 = x+3/x+4
-8
Evaluate the expression. 6^logv6 1.5
1.5 (you can use mathway too)
Find the amount of time required to double an amount at 5.84% if the interest is compounded continuously.
11.87 years
Among various populations of plants or animals, diseases spread exponentially. Use the function y = 8000 (1 - e^-0.03t) to model the spread of Common Corn Rust through a field of 8000 corn plants, with t equal to the number of days since the first case of the disease. How many plants will be infected with Common Corn Rust after 10 days?
2073
Solve each equation. 32^x - 1 = 16^x + 4
21 (you can use mathway too)
Solve logv6 x = 2
36 (you can use mathway too)
Solve 5x^3 - 23x^2 + 29x - 15 = 0.
4/5 +3/5i, 4/5 - 3/5i, 3
Solve. √x+4 = x-2
5
Evaluate each expression. logv3 243
5 (you can use mathway too)
State the number of possible real zeros and turning points of f(x) = x^7 - 6x^6 + 8x^5. Then determine all of the real zeros by factoring.
7 real zeros and 6 turning points; 0, 2, and 4
The world's population is expected to grow at a rate of 1.3% per year until at least the year 2020. In 1994 the total population of the world was about 5,642,000,000 people. Use the formula Pn = P0e^in to predict the world's population Pn, n years after 1994, with P0 equal to the population in 1994 and i equal to the expected growth rate. What is the world's predicted population in the year 2020, rounded to the nearest million?
7,911,000,000
When rabbits were introduced to the continent of Australia they quickly multiplied and spread across the continent since there were only primitive marsupial competitors and predators to interfere with the exponential growth of their population. The data in the following table can be used to create a model of rabbit population growth. 1. Find the regression equation for the rabbit population as a function of time x.2. Write the regression equation in terms of base e.3. Use the equation from part b to estimate the time for the rabbits to exceed 10,000.
IT IS NOT ... 1. y = 7.982 x (1.497)^x 2. y = 7.982e^0.4035x 3. x = 17.7 months
Graph f(x) = 1/4(x-2)^3-8
Put the equation into Mathway.com and select graph, you will get the correct answer
Which is a graph of f(x) = 6x-3/x-1, with any vertical or horizontal asymptotes indicated by dashed lines?
Put the equation into Mathway.com and select graph, you will get the correct answer
Graph f(x) = 2√x+5
Put the equation into Mathway.com and select graph, you will get the correct answer.
Graph f(x) = x(x-4)(x+4)/x^2-8x+12
Put the equation into Mathway.com and select graph, you will get the correct answer.
Graph h(x) = -4x^2
Put the equation into Mathway.com and select graph, you will get the correct answer.
Graph the function f(x) = (1/3)^x
Put the equation into Mathway.com and select graph, you will get the correct answer.
Use the graph of f to describe the transformation that results in the graph of g. f(x) = log x; g(x) = 2logx + 6
The graph of g(x) is the graph of f(x) expanded vertically by a factor of 2, and translated 6 unit(s) up.
Find an exponential function to model the data.
f(x) = 3.56(2.04)^x
Find a logarithmic function to model the data.
f(x) = 60.04 - 8.25 ln x
Use the graph of f to describe the transformation that results in the graph of g. Then sketch the graphs of g and f. f(x) = (1/3)^x ; g(x) = (1/3)^x-2 -4
g(x) is the graph of f(x) translated 2 unit(s) to the right and 4 unit(s) down.
Find the vertical, horizontal, and oblique asymptotes, if any, for f(x) = 3x^3 + 20x^2 + 14x - 65 / x^2 + 8x +15
vertical: x = -5, x = -3 slant: y = 3x - 4
Use the remainder theorem to find which of the following is not a factor of x^3 - 4x^2 - 4x + 16.
x - 12
Determine the solution. 3x-1/4 - x-5/5 > -2
x > -5
List all of the possible rational zeros of f(x) = -3x^4 - 9x^3 - 6x^2 - 8x + 14.
±1, ±2, ±7, ±14, ± 1/3, ± 2/3, ± 7/3, ± 14/3
