Answer:
The value of b to four decimal places is 11.5416
Step-by-step explanation:
The given function is
f(x) = a + b ln(x)
We are also given that f(1) = 6 and f(2) = 14
f(1) = a + b ln(1)
ln(1) = 0
So f(1) = a + b * 0
f(1) = a
=> a = 6
f(2) = a + b ln(2)
f(2) = 6 + b ln(2)
We are given f(2) = 14
=> 6 + b ln(2) = 14
=> b ln(2) = 14 - 6 = 8
=> b = 8/ln(2) = 11.5416
Therefore the value of b to four decimal places is 11.5416
The expression for f(x) is f(x) = 6 + 11.5416 ln(x)
Answer:
b ≈ 11.5416
Step-by-step explanation:
given
f(x) = a + b ln(x)
and f(1) = 6, that is f(x) = 6 when x = 1 , then
6 = a + b ln(1) → [ ln(1) = 0 ]
6 = a
f(x) can now be expressed as
f(x) = 6 + b ln(x)
given
f(2) = 14, that is f(x) = 14 when x = 2 , then
14 = 6 + b ln(2) ( subtract 6 from both sides )
8 = b ln(2) ( divide both sides by ln(2) )
[tex]\frac{8}{ln(2)}[/tex] = b ,so
b ≈ 11.5416 ( to 4 decimal places )