A bacteria culture starts with 1,000 bacteria and doubles in size every 3 hours. Find an exponential model for the size of the culture as a function of time t in hours and use the model to predict how many bacteria there will be after 2 days.

Solve the equation.

$$\frac { 1 } { 2 } x ^ { 2 } + 72 = 0$$

A bacterial culture starts with $500$ bacteria and doubles in size every half hour. How many bacteria are there after $40$ minutes?

Let n be a positive integer. What is the product of all the nth roots of unity?

Find the mean, median, mode, and range of each data set. 12, 22, 33, 34, 44, 44

Write the function in vertex from. Then describe the transformation(s) from the parent function and use the transformations to graph the function.

$$k(x) = -3x^2 + 12x - 7.$$

If you need to drive 30 miles, you have many options. For instance, you can drive 15 miles per hour for 2 hours, 30 miles per hour for 1 hour, or 60 miles per hour for half an hour. Notice that when you double your speed, it takes half as much time to get to your destination. Mathematicians describe this kind of relationship as an inverse variation. Why do you suppose they use the word inverse to describe it?

Solve each equation:

a. 15 log 6x = -15

b. log (-7x) = 3

c. 3 log 10x = -6

d. -log 4x = -2

Simplify and state any restrictions on the variables. a) $\log (2 m+6)-\log \left(m^{2}-9\right)$ b) $\log \left(x^{2}+2 x-15\right)-\log \left(x^{2}-7 x+12\right)$

Write a numerical expression for each of the following. Then find the sum. You save $200, and then spend$75.

Classify the number as a member of one or more of the following sets: the rational numbers, the integers, the natural numbers, the irrational numbers.

$$2\sqrt{7}$$

Assume that the random variable X is normally distributed, with mean $\mu$=50 and standard deviation $\sigma$=7. Compute the following probabilities. Be sure to draw a normal curve with the area corresponding to the probability shaded. P(X>35)

Identify the following events as independent or dependent. a. Reachjng into a drawer in the dark, pulling out one sock, and then reaching back in and pulling out another. b. Selecting a dog biscuit for your dog, feeding it to her, and then getting another one. c. Rolling a 3 on each of two dice that are tossed at the same time. d. Spinning a 5 on a spinner and then spinning again and getting a 4.

A burst of compressed air pushes a pellet out of a blowpipe. The force exerted by the air on the pellet is given by $F ( t ) = F _ { 0 } e ^ { - t / \tau }$, where $\tau$ is called a time constant because it has units of time. (a) What does $F _ { 0 }$ represent? (b) What is the momentum of the pellet after an interval equal to one time constant has elapsed? (c) What is the momentum after an interval equal to five time constants has elapsed? (d) What is the final momentum of the pellet after a long time interval has elapsed? (e) If $\tau = 0.50 \mathrm { ms }$, after how long a time interval has the momentum reached 95% of its final value?