Question

A small company is selling a new product, and they need to know how many to produce in the future in order to make a profit and revenue.

After 12 months, they sold 4 thousand products; after 18 months, they sold 7 thousand products; and after 36 months, they sold 15 thousand products.
1. Based on this information, estimate the number of products sold after 48 months.
2. Is the number of products sold a function of the amount of months? Does this information show a linear function? Explain your thinking.

Answer 1

1. To estimate the number of products sold after 48 months, we can assume that the sales follow a linear pattern over time. We can use the data given to find the rate of change (slope) of the line and then use that to predict the sales after 48 months.

Using the points (12, 4), (18, 7), and (36, 15), we can find the slope of the line that represents the sales:

slope = (15 - 7) / (36 - 18) = 8 / 18 = 4/9

Now we can use the point-slope form of a line to find the equation of the line:

y - 4 = (4/9)(x - 12)

where x is the number of months and y is the number of products sold.

To find the estimated number of products sold after 48 months, we can substitute x = 48 into the equation and solve for y:

y - 4 = (4/9)(48 - 12)

y - 4 = 16

y = 20

Therefore, we can estimate that the company will sell 20 thousand products after 48 months.

2. Yes, the number of products sold is a function of the amount of months. It is a linear function because the sales appear to follow a straight line over time, as we assumed in our calculation above. This means that for every increase of 1 month, the number of products sold increases by a constant rate of 4/9 thousand.

Explanation: