Exam 4: Living in a Nonlinear World

Find the vertex of the parabola.

Simplify. Write your answer in exponent form.

Solve the equation by using the quadratic formula. $x ^ { 2 } + 7 x - 8 = 0$

Linda deposited $3500 in an account that pays 5 1/2 % simple interest for 4 years. a. How much interest will she earn in 4 years? b. What will be the total value of the account after 4 years?

Write the number in scientific notation. A red blood cell is about 0.000007 meters in diameter.

Identify a and determine if the parabola opens upward or downward.

Josephine deposited $8,000 in an account that pays 6% compounded annually. Complete the table to determine the amount of her investment at the end of 3 years. Year Interest Total 1st 2nd 3rd

Use the commutative and associative properties of real numbers and the properties of exponents to simplify the expression.

Once an antibiotic is introduced to bacteria, the number of bacteria decreases exponentially. For example, beginning with 1 million bacteria, the amount present t days from the time penicillin is introduced is given by the function Rounding to the nearest thousand, determine how many bacteria are present after 6 days.

Simplify the expression. Write the answer in exponent form.

Factor the polynomial completely. $x ^ { 2 } y ^ { 2 } - 9 x ^ { 2 } - 16 y ^ { 2 } + 144$

Find the total amount for the investment using compound interest.

Subtract the polynomials.

Carla deposited $12,400 into an account paying 4% simple interest 5 years ago. If she withdraws the entire amount of money, how much will she have?

Simplify the expression. Write the answer in exponent form. $y ^ { 3 } \cdot y ^ { 5 } \cdot y ^ { 7 } \cdot y ^ { 9 }$

Clear parentheses and combine like terms.

The following table shows the U.S. population for the years 1920-2000. a. Determine whether the equation of best fit for this data will be quadratic or exponential, and find the equation of the best fit. Round coefficients to 4 decimal places. b. What is the y-intercept and what does it represent? c. Would an x-intercept make sense in this case? If so, find it. If not, explain why not. d. At approximately what rate is the U.S. population growing? e. Use the equation to estimate the U.S. population in 2013. Round to the nearest tenth of a million. f. Using the equation, when will the U.S. population break 400 million?

Add the polynomials. $\left( \frac { 7 } { 2 } y ^ { 3 } + 2 y - \frac { 1 } { 4 } \right) + \left( 2 y ^ { 3 } - 4 y ^ { 2 } + \frac { 21 } { 2 } \right)$

Write the number in scientific notation.

a. When does the ball hit the ground? Round to the nearest tenth of a second. b. What is the highest height the ball reaches, and when?