Question

The solution to this system of equations lies between the x-values 0 and 2. Using up to three iterations of successive approximation, find an approximate x-value representing the solution to the system.
y = 4^x-1
y = (1/2)^x-2

The approximate solution to this system of equations is
A. 1.375
B. 1.875
C. 1.5

Answer 1

Answer:

The approximate solution of the given system of equations is $1.333$.

Step-by-step explanation:

The given equations are

$y=4^{x-1}$                       ..... (1)

$y=(\frac{1}{2})^{x-2}$         .... (2)

Equate both functions to find the intersection point of both function.

$4^{x-1}=(\frac{1}{2})^{x-2}$

$(2^2)^{x-1}=(2^{-1})^{x-2}$

Use $a^{mn}=(a^m)^n$ property of exponent.

$2^{2x-2}=2^{-x+2}$

Since the base is same, therefore compare the exponents.

$2x-2=-x+2$

$3x=4$

$x=\frac{4}{3}$

$x=1.333$

Therefore the approximate solution is $1.333$.

Answer 2

Using a graphing caluculator (TI 83/84):
y(sub1) = 4^(x - 1)
y(sub2) = (1/2)^(x - 2)
Graph the equations.
To find the point of intersection: 2nd CALC #5
x = 1.3

I only did 1 iteration but 2 more will only make it more accurate.