Given an equation of the form
for
use a graphing calculator to approximate the solution.
Press
[Y=] . Enter the given exponential equation in the line headed “
Y
1 = ”.
Enter the given value for
in the line headed “
Y
2 = ”.
Press
[WINDOW] . Adjust the
y -axis so that it includes the value entered for “
Y
2 = ”.
Press
[GRAPH] to observe the graph of the exponential function along with the line for the specified value of
To find the value of
we compute the point of intersection. Press
[2ND] then
[CALC] . Select “intersect” and press
[ENTER] three times. The point of intersection gives the value of
x for the indicated value of the function.
Approximating the solution of an exponential equation
Solve
graphically. Round to the nearest thousandth.
Press
[Y=] and enter
next to
Y
1 =. Then enter 42 next to
Y2= . For a window, use the values –3 to 3 for
and –5 to 55 for
Press
[GRAPH] . The graphs should intersect somewhere near
For a better approximation, press
[2ND] then
[CALC] . Select
[5: intersect] and press
[ENTER] three times. The
x -coordinate of the point of intersection is displayed as 2.1661943. (Your answer may be different if you use a different window or use a different value for
Guess? ) To the nearest thousandth,
While horizontal and vertical shifts involve adding constants to the input or to the function itself, a
stretch or
compression occurs when we multiply the parent function
by a constant
For example, if we begin by graphing the parent function
we can then graph the stretch, using
to get
as shown on the left in
[link] , and the compression, using
to get
as shown on the right in
[link] .
the transfer of energy by a force that causes an object to be displaced; the product of the component of the force in the direction of the displacement and the magnitude of the displacement
A wave is described by the function D(x,t)=(1.6cm) sin[(1.2cm^-1(x+6.8cm/st] what are:a.Amplitude b. wavelength c. wave number d. frequency e. period f. velocity of speed.
A body is projected upward at an angle 45° 18minutes with the horizontal with an initial speed of 40km per second. In hoe many seconds will the body reach the ground then how far from the point of projection will it strike. At what angle will the horizontal will strike
Suppose hydrogen and oxygen are diffusing through air. A small amount of each is released simultaneously. How much time passes before the hydrogen is 1.00 s ahead of the oxygen? Such differences in arrival times are used as an analytical tool in gas chromatography.
the science concerned with describing the interactions of energy, matter, space, and time; it is especially interested in what fundamental mechanisms underlie every phenomenon
