draw the solution curve P(t) that satisfies the initial condition P(0)=75

1. a) f(x) is a quadratic function. The graph f(x) decreases on the interval (-∞, -2) and increases on the interval (-2, 0). It has a y-intercept at (0, 4). What is a possible equation for f(x)? b) Is there only one quadratic function, f(x), that has the characteristics given in part a)?

The end-of-year assets of the Medicare Hospital Insurance Trust Fund (in billions of dollars) for the years 2006 through 2014 are shown. (a) Use the regression capabilities of a graphing utility to find a model of the form          M = at3 + bt2 + ct + d for the data. Let t = 6 represent 2006. (b) Use a graphing utility to plot the data and graph the model. (c) Find the maximum value of the model and compare the result with the actual data.

#3:

7. York Region introduced a program to support the population of deer in its forests. After t years of protection, the deer population in York Region can be modelled by the function P(t)= (t²-2t-35)² + 2000. (a) Find the deer population at the beginning of the protection program. (b) Find the maximum deer population over the 10 years of the protection program.

4. Find the maximum of the function f(x) = 100-(10 – x1)? – (5 – x2)² by Simplex Method. Take initial coordinates as: (0,0), (2,0), (0,2)

(Use Techology to draw graph) If a projectile is fired into the air, its height above ground at any time is given by the forumula y = y0 + v0t - 1/2gt2,   where  y = height above ground at time t, y0 = initial height above ground at time t=0, v0 = initial velocity at time t = 0, g = acceleration due to gravity, t = time passed since projectile's firing. If a projectile is launched with an initial velocity of 100 meters per second (100 m/s) from a rooftop 8 meters (8m) above ground level, at what time will the projectile first reach a height of 400 meters (400m)? Draw the grap using technology (show steps). Note: Near the earth's surface, the acceleration due to gravity is approximately 9.8 meters per second per second (9.8 (m/s)s or 9.8 m/s2).

USE THIS SPACE FOR SCRATCH WORK. ): The population of doves within a certain forest can be modeled by the equation nt P(t) = 445 - 112cos 12 where t is the number of months since January 1990. When is the population at its maximum? (A) January of every year (B) January of every even-numbered year (C) January of every odd-numbered year (D) July of every even-numbered year (E) July of every year