g Since we know the number of zombies is growing proportionally to the number of zombies present, we can construct a differential equation which models the number of zombies P(t): dP dt = kP. Specify the initial condition(s) of the differential equation. 2. From Example 5 in section 1.1, we learn that the general solution of the above differential equation takes form P(t) = Cekt. Use the following Mathematica command to define a function: P[t ] = C ∗ Eˆ(k ∗ t), and check the value of P(t) at t = 0, 1, 20 (days) by putting in P[0], P[1] and P[20]. 3. Verify P(t) we defined above is the general solution of the differential equation in Problem 1 by plugging P(t) into the differential equation: Simplify[P 0 [t] − k ∗ P[t]]. The Simplify function asks Mathematica to simplify the expression. Based on the result of the command, do you think P(t) is the general solution? 4. Use Solve and the initial conditions to find the unknown consta

Which of the following contains a variable?

Which of the following best describes the graph below? + + 2 + 3 + 4 1 o a. it is not a function. o b. it is a one-to-one function. o c. it is a many-to-one function. o d. it is a function, but it is not one-to-one.

Time (minutes) amount of water (gallons) practice 1. jin fills up a 510-gallon pool in the backyard for her children. she fills it with the garden hose at a rate of 17 gallons per minute. after it is filled, she lets it sit for 30 minutes in order to let the water temperature rise. the children then get in and have fun for an hour. the pool loses about 5 gallon of water each minute due to their splashing and playing. at the end of the hour, they tear the pool while getting out, which causes a leak the pool then begins to lose water at a rate of 2 gallons per minute. a. complete the table to show the amount of water in the pool after each minute. b. create a graph to model the problem situation. include when the pool will be empty. c. write a piecewise function that models this problem situation. explain your reasoning for each piece of the function. d. identify the x- and y-intercept. explain what they mean in terms of the problem situation, atamantha a cul 80 100 120 150 200 ning, inc