Question 420145: FUN industries started with 300,000 dollars. Each year for 10 years, the company lost 20,000 dollars due to a lawsuit. A new company, WIN Corparation started with 30,000 dollars and earned 25% each year for 10 years. Between what 2 years would WIN surpass FUN? If these trends stayed constant...What year would FUN go bankrupt and when wuold WIN earn 1 million dollars?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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:
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.
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