Question 420145
formula for FUN is:


y = -20,000 * x + 300,000


formula for WIN is:


y = 30,000 * 1.25^x


they both start at year 0.


in 10 years, FUN will have 300,000 - 20,000 *  10 = 100,0000 


in 10 years, WIN will have 30,000 * 1.25^10 = 279,396.7724


you can graph these 2 equations to see what year their fortunes cross.


the graph is shown below:


{{{graph(600,600,-1,11,-100000,400000,-20000*x + 300000,30000*1.25^x)}}}


the graph shows that their fortunes cross sometime between the 7th year and the 8th year.


to find the exact point that they cross, we set the 2 formulas equal to each other and solve for the break even point.


first formula is y = 300,000 - 20,000 * x
second formula is y = 30,000 * 1.25^x


when x = 7, first formula gets  you 300,000 - 20,000 * 7 = 300,000 - 140,000 = 160,000.

when x = 7, second formula gets you 30,000 * 1.25^7 = 30,000 * 4.768371582 = 143,051.1475.


first formula give you a higher amount.


when x = 8, first formula gets you 300,000 - 20,888 * 8 = 300,000 - 160,000 = 140,000.


when x = 8, second formula gets you 30,000 * 1.25^8 = 30,000 * 5.960464478 = 178,813.9343.


Their fortunes flip somewhere in between the 7th and the 8th year.


from the graph, it can be seen that the actual break even point will be closer to the 7th year than the 8th year.