IB Mathematics Applications and Interpretation Quiz
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An engineering model is described by the equation
x
3
+
ln
(
x
)
=
5
x^3 + \ln(x) = 5
x
3
+
ln
(
x
)
=
5
. To solve this equation for
x
>
0
x > 0
x
>
0
, an iterative formula is proposed:
x
n
+
1
=
5
−
ln
(
x
n
)
3
x_{n+1} = \sqrt[3]{5 - \ln(x_n)}
x
n
+
1
=
3
5
−
ln
(
x
n
)
.
Using a starting value of
x
0
=
1.5
x_0 = 1.5
x
0
=
1.5
, find the solution to the equation correct to four significant figures.
A
1.649
B
1.663
C
1.671
D
1.705
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