Activity 1.3.4. A rapidly growing city in Arizona has its population P at time t, where t is the number of decades after the year 2010, modeled by the formula P(t) = 25000e /5. Use this function to respond to the following questions. a. Sketch an accurate graph of P for t = 0 to t = 5 on the axes provided in Fig- ure 1.3.11. Label the scale on the axes carefully. y Figure 1.3.11: Axes for plotting y = P(t) in Activity 1.3.4.

Use your schools library, the Internet, or some other reference source to find real-life applications of approximations of functions.

Use the table of values you made in part 4 of the example to find the limiting value of the average rate of change in velocity.

For a person at rest, the velocity v (in liters per second) of airflow during a respiratory cycle (the time from the beginning of one breath to the beginning of the next) is modeled by v=0.85sint/3, where t is the time (in seconds). a Find the time for one full respiratory cycle. b Find the number of cycles per minute. c Sketch the graph of the velocity function. Use the graph to confirm your answer in part a by finding two times when new breaths begin. (Inhalation occurs when v0, and exhalation occurs when v0.)

bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.

Earthquake the graph shows the vertical acceleration of the Ground from the 1994 Northridge earthquake in Los Angles, as measured by a seismograph. (Here t represents the time in seconds.) (a) At what time t did the earthquake first make noticeable movement of the Earth? (b) At what time t did the earthquakes seem to end? (c) At what time t was the maximum intensity of the earthquake list reached

Sketch the graph of fx=5e0.17x.