Calculus Word Problem: Which is the best investment?

Question

You have two investment options available to you. In option A, Money Group will take the amount invested, square it, and then multiply by 350 to produce the amount paid to the investor. In option B, Money Makers Inc. will raise 1.43 to the power of the amount invested in order to produce the amount paid to the investor. Which option would you choose and why?

Answer 1

depends on how much you are investing.

option A you get:   y = 350x^2

option B you get:   y = 1.43^x

so clearly, for larger sums option B will win but for smaller sums option A will win.  to figure out where the point where it goes from A to B, simply set the equations equal to each other and solve:

1.43^x = 350x^2

...natural log of both sides

x ln (1.43) = 2 ln (x) + ln(350)

...you can solve from here

Answer 2

1.43 ^ of amount infested for anything 37 and above

amount invested ^2 * 350 for anything below 37