the total sales made by a salesperson was $25,000 after 3 months and $68,000 after 23 months. predict the total sales after 41 months.

Question

i will be so grateful if anyone can help me

Answer 1

This is a linear relationship. We can solve using the point-slope form of a line. Let x be the number of months and y is the amount in sales.

First, we need to find the slope of the line. We can do this by using points on the line at (3,25000) and (23,68000). To find the slope of a line (m), we use the following equation

m= (y₂ - y₁) / (x₂ - x₁)

m= (68000-25000) / (23-3)

m= 2,150

Now, we can use the point-slope form of a line and one of our points to solve.

point-slope form: y - y₁ = m(x-x₁)

Using point (3,25000), we can plug in and solve.

y - 25,000 = 2,150(x-3)

y - 25,000 = 2,150x - 6,450

y = 2,150x + 18,550

So, the equation of our line is y = 2,150x + 18,550. Now we can plug in our x value of 41 months into the equation to predict the total sales after 41 months.

y = 2,150(41) + 18,550

y = $106,700

After 41 months, we predict the sales amount to be $106,700

Answer 2

To predict, we would assume a linear model. In the 20 month period from 3 to 23 months, the total sales increased by $43000, or $2150 per month. After 18 more months from 23 to 41 months, the total sales would increase by 18 * $2150 = $38,700, for a grand total of $81,700.