Question

A group of computer engineers secured a loan to fund a new startup in Silicon Valley. The bank gives them a loan in the amount of 1.8​one point eight million dollars. The engineers estimate that their business will be able to make a profit of approximately $0.6​zero point six million per year. They keep track of their debts, profits, and overall financial status on a balance sheet. They enter the debt as a negative value and all profits as positive values.
Define a unit for the amount of time since the company began. Enter a variable for the amount of time since the company began and use this variable to write an expression for the expected financial status.
What was the financial status of the company when it began?
If the estimates were correct, how many years was it before the financial status of the company was 11.4​eleven point four million dollars?
After completing the worksheet, graph your model.

Answer 1

It will take the company 20.3 years to have a financial worth of $11.4

The unit of the amount of time

The estimate of profit is given as;

Profit = $0.6 million per year

This means that the engineers based their estimate per year

Hence, the unit of time is year

The variable of the amount of time

To do this, we make use of any variable of our choice.

In this case, we let x represents the variable of the amount of time.

Expression for the expected financial status

In (a), we have:

Profit = $0.6 million per year

So, the expected financial status is 0.6x

The financial status of the company when it began

This is the amount taken as loan by the engineers.

So, the financial status at the beginning is 1.8

Years to attain the financial status of $11.4 million?

Using the expressions above, we have the yearly worth to be:

y = 0.6x - 1.8

When the financial status is $11.4 million, we have:

0.6x - 1.8 = 11.4

Evaluate the like terms

0.6x = 12.2

Divide both sides by 0.6

x = 20.3

Hence, it will take the company 20.3 years to have a financial worth of $11.4

The graph of the model

See attachment for the graph of y = 0.6x - 1.8

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