Video Transcript
The value of the amount of money 𝑛 years after it has been invested in a project is given by the function 𝑝 of 𝑛 equals 100𝑛 plus 1000. What does the number 1000 represent in the function?
We have the function 𝑝 of 𝑛 equals 100𝑛 plus 1000. We know that this function is telling us the value of the amount of money 𝑛 years after it has been invested. So we can say that 𝑝 of 𝑛 equals the value of money 𝑛 years after it has been invested. 𝑛 is the number of years. We’re multiplying 100 by the number of years that money has been invested. And then that value is added to 1000.
What then can we say about 1000? This 1000 is not being multiplied by the number of years in the account. And so we can say that this 1000 is the initial investment amount in dollars. 1000 dollars was put into an account, invested. Each year, 100 dollars is added to it. And 𝑝 of 𝑛 is the value of the amount of that money 𝑛 years after it was invested.
We could think about this question in the 𝑥𝑦 plane. We could rewrite our function to say 𝑦 equals 100𝑥 plus 1000. This is in the form 𝑦 equals 𝑚𝑥 plus 𝑏. We know that 𝑏 equals the 𝑦-intercept. In this case, the 𝑦-intercept is 1000. When 𝑥 is zero, when zero years have passed, 𝑦 equals 1000. And every year after that, 100 dollars is added. Looking on the graph, it’s easy to see why this 1000 dollars represents the initial investment. It’s the starting amount before any interest is added.
