A coordinate system is placed at the center of a town with the positive x -axis pointing east, and the positive y -axis pointing north. A cell tower is located 4 mi west and 5 mi north of the origin. a. If the tower has a 8 -mi range, write an inequality that represents the points on the map serviced by this tower. b. Can a resident 5 mi east of the center of town get a signal from this tower?
A coordinate system is placed at the center of a town with the positive x -axis pointing east, and the positive y -axis pointing north. A cell tower is located 4 mi west and 5 mi north of the origin. a. If the tower has a 8 -mi range, write an inequality that represents the points on the map serviced by this tower. b. Can a resident 5 mi east of the center of town get a signal from this tower?
Solution Summary: The author calculates an inequality that describes the points on the map serviced by a cell tower if it has 8 miles of range and the tower range is 8mi.
A coordinate system is placed at the center of a town with the positive
x
-axis
pointing east, and the positive
y
-axis
pointing north. A cell tower is located
4
mi
west and
5
mi
north of the origin.
a. If the tower has a
8
-mi
range, write an inequality that represents the points on the map serviced by this tower.
b. Can a resident
5
mi
east of the center of town get a signal from this tower?
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
3. We'd like to know the first time when the population reaches 7000 people. First, graph the
function from part (a) on your calculator or Desmos. In the same window, graph the line y =
7000. Notice that you will need to adjust your window so that you can see values as big as
7000! Investigate the intersection of the two graphs. (This video shows you how to find the
intersection on your calculator, or in Desmos just hover the cursor over the point.) At what
value t> 0 does the line intersect with your exponential function? Round your answer to two
decimal places. (You don't need to show work for this part.) (2 points)
Suppose the planet of Tattooine currently has a population of 6500 people and an annual growth rate of
0.35%. Use this information for all the problems below.
1. Find an exponential function f(t) that gives the population of Tattooine t years from now. (3
points)
A house was valued at $95,000 in the year 1988. The value appreciated to $170,000 by the year 2007.
A) If the value is growing exponentially, what was the annual growth rate between 1988 and 2007?
Round the growth rate to 4 decimal places.
r =
B) What is the correct answer to part A written in percentage form?
r = 3
%.
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