Question

You work for a robotics company that is making a new line of hamburger-making robots to be sold to fast-food chains. This is a big-ticket item, so sales will be slow at first, but should pick up over time. Your marketing department estimates that the sales growth rate will increase linearly by 2 robots per month per month. In the first month (t 0), for which you have already booked sales for 10 units, the growth rate is expected to be 5 robots per month. How many total robots do you expect to sell by the end of the tenth month (t = 9)?

Answer 1

565 robots

Explanation:

We can do this numerically, month by month:

At t = 0, sale is 10 units. Growth rate is 5 robots per month.

At t = 1, sale is 15 units. Growth rate is 7 robots per month.

At t = 2, sale is 22 units. Growth rate is 9 robots per month.

At t = 3, sale is 31 units. Growth rate is 11 robots per month.

At t = 4, sale is 42 units. Growth rate is 13 robots per month.

At t = 5, sale is 55 units. Growth rate is 15 robots per month.

At t = 6, sale is 70 units. Growth rate is 17 robots per month.

At t = 7, sale is 87 units. Growth rate is 19 robots per month.

At t = 8, sale is 106 units. Growth rate is 21 robots per month.

At t = 9, sale is 127 units. Growth rate is 23 robots per month.

So the total robots we can expect to sell by the end of tenth month is

565 robots.