Question

In one year the sales of a company increase at a constant rate. At 2 months the company sells 12 products, and after 8 months the company sells 30,000 products. (At t-0, the company does not necessarily have 0 sales)

a. Write an equation to model the situation.
b. If the company's sales continue to increase at the same rate, how long would it take before the company reached 145,000 sales? (Calculator permitted-round to 3 decimal places)

Answer 1

The answer is below

Step-by-step explanation:

a) Since sales of the company increases at a constant rate, it means that the function is a linear function. Let the time in months be the independent variable x and the sales be the dependent variable y. It can be represented as (x, y)

At 2 months the company sells 12 products, this can be represented by (2, 12). Also after 8 months the company sells 30,000 products, this can be represented by (8, 30000). The formula for a linear function is:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Using (2, 12) and (8, 30000):

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)\\\\y-12=(30000-12)/(8-2)(x-2)\\ \\y-12=4998(x-2)\\\\y-12=4998x-9996\\\\y=4998x-9984`

b) For a sales of 145000, i.e y = 145000

y = 4998x - 9984

145000 = 4998x - 9984

4998x = 145000 + 9984

4998x = 154984

x = 31.009

It would take about 31.009 months to make a sales of 145000