Question

5. ** Saskatchewan Widgets and Manitoba Widgets are two companies that were founded at the same time. Saskatchewan Widgets started 10 million dollars in debt, and they make a constant yearly profit. After 5 years, they were 6 million dollars in debt. The graph of the balance (in millions of dollars) of Manitoba Widgets as a function of time (in years) is shown below.

Answer 1

We know that Saskatchewan started with 10 million dollars in debt.

According to the graph, Manitoba started with 8 million dollars in debt.

Hence, Manitoba Widgets started with a greater balance because -8 million is greater than -10. (a)

According to the problem, after 5 years, Saskatchewan had 6 million dollars in debt. So, let's find the rate

`r=(-6-(-10))/(5)=(-6+10)/(5)=(4)/(5)`

This means the debt is decreasing by 4 million every 5 years.

Now, we find the rate of Manitoba using the points (0,-8) and (4, -5).

`m=(-5-(-8))/(4-0)=(-5+8)/(4)=(3)/(4)`

This means Manitoba's debt is decreasing by 3 million every 4 years.

Hence, Saskatchewan Widgets makes a greater yearly profit. (b)