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Answer:
The function f(x) is represented by:
Hence, a=1500 and b=0.97
Step-by-step explanation:
The patient currently has a bone density of 1,500 kg/mg^3.
A doctor estimates that a particular patient is losing bone density at a rate of 3% annually.
This means that the bone density that is remaining is:
100-3=97%
which is also represented as: 97%=97/100=0.97
Hence, the function f(x) that represents the bone density after x years is represented by:
where a is the initial bone density which is given to be: 1500 kg/mg^3.
Hence, the function is:
Step-by-step explanation:
There are certain methods for solving a system of equations. Some of which are:
- Substitution Method
- Elimination Method
- Graphing Method
<em>Substitution Method</em>
Substitution method to solve a system of equations is suitable if a variable of a any equation seems isolated or could comfortably be isolated without any ration/fraction resulting.
For example, for the following system of equations
x - 2y = 11....[A]
x = 5 - y....[B]
substituting the value of x = 5 - y from equation [B] into equation [A], so that
(5 - y) - 2y = 11
5 - y - 2y = 11
3y = -6
y = -2
<em>Elimination Method</em>
Elimination method to solve a system of equations is suitable if both equation are in standard form, and just adding or subtracting the equations to determine an equation in one variable.
For example, for the following system of equations
2x + 7y = -5....[C]
5x - 7y = 12....[D]
Adding Equation [C] and Equation [D].
7x + 0 = 7
x = 1
<em>Graphing Method</em>
Sometimes graphing method may be used to solve the system of the equation and visualize the solution.
For example,
y = -2....[E]
y = 3x + 1....[F]
The solution for this system of equation is the point of intersection of both the lines, which is shown in attached figure. The point of intersection is (-1, -2).
Hence, the solution of this system of equations is (-1, -2), as shown in attached figure.
<em>Keywords: system of equations, elimination method, substitution method, graphing method</em>
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