Step 1
Rewrite the equation so that it equals zero on one side.
2ˣ - 4 = 3⁻ˣ - 2
(2ˣ - 4) - (3⁻ˣ - 2) = 0
Step 2
Evaluate the rewritten equation at the lower and upper bounds. To find the solution that lies between 1 and 2, set these values as the lower and upper bounds while finding the solution.
(2⁽¹⁾ - 4) - (3⁽⁻¹⁾ - 2) ≈ -0.333
(2⁽²⁾ - 4) - (3⁽⁻²⁾ - 2) ≈ 1.889
Step 3
Take the average of the lower and upper bounds.
(1 + 2)/2 = 3/2
Step 4
Evaluate the rewritten equation at x = 3/2
(2⁽³/²⁾ - 4) - (3⁽⁻³/²⁾ - 2) ≈ 0.636
Step 5
Since this value is positive, replace the previous lower bound so that the bounds are now x = 3/2 and x = 2.
Where did Jacob make a mistake, and what was the error?
A. Jacob made a mistake at step 5. He should have used x= 3/2 as the new upper bound.
B. Jacob made a mistake at step 2. The actual evaluation of the rewritten equation at x=2 is 3.
C. Jacob did not make any mistakes in the calculation process.
D. Jacob made a mistake at step 4. The actual evaluation of the rewritten equation is approximately -1.636
