Answer: 9 year (approx)
Step-by-step explanation:
Since, In the Investment R,
The initial amount = $500
Which is increasing by $45 per year,
Thus, the total amount after x years in investment R = 500 + 45 x
In the investment Q,
The initial amount = $400
Which is increasing by 10% per year,
Thus, the total amount after x years in investment Q = ![400( 1 + \frac{10}{100})^x = 400(1+0.1)^x = 400(1.1)^x](https://tex.z-dn.net/?f=400%28%201%20%2B%20%5Cfrac%7B10%7D%7B100%7D%29%5Ex%20%3D%20400%281%2B0.1%29%5Ex%20%3D%20400%281.1%29%5Ex)
Since, the intersection point of the equations y =500+45x and y = 400(1.1)^x
are (-6.178, 221.992) and (8.069, 863.12)
But we can not take a negative number as a number of year,
Thus, the year in which both investment will equal is 8.069
After that the investment Q will be exceed the investment R,
⇒ The first year at which the investment Q will be exceed the investment R is approx 9th year.