A wolf population is growing exponentially. In 2011,
wolves were counted. By
the population had reached 236 wolves. What two points can be used to derive an exponential equation modeling this situation? Write the equation representing the population
of wolves over time
Writing an exponential model when the initial value is not known
Find an exponential function that passes through the points
and
Because we don’t have the initial value, we substitute both points into an equation of the form
and then solve the system for
and
Substituting
gives
Substituting
gives
Use the first equation to solve for
in terms of
Substitute
in the second equation, and solve for
Use the value of
in the first equation to solve for the value of
Thus, the equation is
We can graph our model to check our work. Notice that the graph in
[link] passes through the initial points given in the problem,
and
The graph is an example of an
exponential decay function.
Do two points always determine a unique exponential function?
Yes, provided the two points are either both above the x-axis or both below the x-axis and have different x-coordinates. But keep in mind that we also need to know that the graph is, in fact, an exponential function. Not every graph that looks exponential really is exponential. We need to know the graph is based on a model that shows the same percent growth with each unit increase in
which in many real world cases involves time.
Given the graph of an exponential function, write its equation.
First, identify two points on the graph. Choose the
y -intercept as one of the two points whenever possible. Try to choose points that are as far apart as possible to reduce round-off error.
If one of the data points is the
y- intercept
, then
is the initial value. Using
substitute the second point into the equation
and solve for
If neither of the data points have the form
substitute both points into two equations with the form
Solve the resulting system of two equations in two unknowns to find
and
Write the exponential function,
Writing an exponential function given its graph
Find an equation for the exponential function graphed in
[link] .
We can choose the
y -intercept of the graph,
as our first point. This gives us the initial value,
Next, choose a point on the curve some distance away from
that has integer coordinates. One such point is
Because we restrict ourselves to positive values of
we will use
Substitute
and
into the standard form to yield the equation
A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
