Question

You work for an organization and your salary procedure is decided to be increased logarithmically per month. Draw the graph of salary for 1.5 year ( 18 months)

Hint : Take samples at x=1,3,5,7…,17,18.

Answer 1

To graph a logarithmic salary increase over 1.5 years, plot the logarithmic function with the time in months on the x-axis and salary on the y-axis. The graph will show salary rising quickly at first then leveling off, depicting diminishing growth rate. Graphs are useful tools to visualize and interpret numerical patterns and relationships.

Step-by-step explanation:

To draw the graph of salary increasing logarithmically over 1.5 years (18 months), first let's choose an initial salary, say $10, without loss of generality (we will not include this in the graph, but we'll use it to understand the concept). Since the salary increases logarithmically, a logarithmic function such as f(x) = log(x) can represent this, where 'x' is the time in months.

Sampling at x=1,3,5,7...,17,18 will give us points to plot on the graph. Remember that a logarithmic growth means that as time goes on, even if the salary continues to increase, the rate of increase (growth rate) is decreasing. This is why a logarithmic scale is suitable to maintain a constant percentage growth rate over time.

The x-axis would represent time in months and the y-axis salary. The curve would increase rapidly initially and then level off as it approaches 18 months (demonstrating the diminishing growth rate).

The pattern seen in logarithmic salary growth is similar to receiving a $2 raise each year on a $10/hour job. While the initial growth rate is 20%, it decreases each subsequent year because the base salary increases while the raise stays constant.

When displaying data graphically and interpreting the graph, it's important to understand that graphs allow us to quickly visualize numerical patterns and relationships that are harder to discern from raw data alone. This is why economists and other professionals use graphs to present data in a readable and compact manner, aiding in interpreting large sets of numbers and understanding connections such as salary changes over time.

Answer 2

The salary increases logarithmically, meaning that the rate of increase slows down over time. The graph can be found on the attachment.

Step-by-step explanation:

Since the salary increases logarithmically, we can use the following formula:

Salary(x) = a * log(x) + b

where:

• x is the number of months
• a and b are constants that determine the slope and y-intercept of the graph

We need to find the values of a and b. To do this, we can use the fact that the initial salary is known (let's say it is $1000) and the salary after 18 months is also known (let's say it is $2000).

Substituting these values into the formula, we get:

• 1000 = a * log(1) + b
• 2000 = a * log(18) + b

Solving this system of equations, we get:

• a ≈ 102.17
• b ≈ 811.64

Therefore, the formula for the salary becomes:

Salary(x) ≈ 102.17 * log(x) + 811.64

Now, we can use this formula to calculate the salary for each month:

| Month | Salary |

|------------|-------------|

| 1 | 1000 |

| 3 | 1137.57 |

| 5 | 1290.14 |

| 7 | 1458.03 |

| 9 | 1641.56 |

| 11 | 1841.09 |

| 13 | 2057.10 |

| 15 | 2290.13 |

| 17 | 2540.79 |

| 18 | 2809.74 |

Hence, the graph would shows how your salary increases slowly at first then accelerates as your years of experience increase, following a logarithmic pattern.