Question

MONEY Jarvis has been offered a new job. He is trying to make predictions about how much he might earn at his current job in future years to see if he should accept the new offer or stay at his current job. Use the table showing his salary for the past 7 years to write the logarithmic function that best fits the data. Round to the nearest ten-thousandth, if necessary.

Answer 1

The form of the required logarithm function is the general form of a

logarithm function in which the type of logarithm is the natural logarithm.

The logarithmic function that best fits the data is presented as follows;

• Equation y = 42 + 14.267·㏑ x

Derivation method

The logarithmic function can be presented as follows;

$y = \mathbf{ a + b \cdot ln \, x}$

Where;

x = The year

y = Salary (thousands of dollars)

From the given values, we have;

When x = 1, $ln\, 1$ = 0

y = 42

Therefore;

$b \cdot ln \, 1 = 0$

y = a + 0 = a = 42

When x = 2, we have;

$52 = \mathbf{42 + b \cdot ln \, 2}$

$52 - 42 = b \cdot ln \, 2$

10 = $b \cdot ln \, 2$

$b = \dfrac{10}{ln \, 2} \approx \mathbf{ 14.267}$

• The logarithmic function is; y = 42 + 14.267 ㏑ x

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