If you gave 1000 dollars the first day 2000 the second day 3000 the third day and so on how many days would it take to get a million dollars?

Answer 1

The graph that you use is parabolic. Use the quadratic function y=ax^2 + bx + c and three points to find the equasion you would need to use.

Points are as follows, (day(x), money(y))

(0,0) day zero start wth nothing

(1,1000) day 1, 1000

(2,3000) day 2, 2000 plus previous days

y = a(x)^2 + b(x) + c

using first point:

0 = a(0)^2 + b(0) + c

0 = c

using second point, and c from above:

1000 = a(1)^2 + b(1) + (0)

1000 = a + b

1000 - a = b

using third point and b and c from above:

3000 = a(2)^2 + (1000 - a)(2) + (0)

3000/2 = (4a + 2(1000 - a))/2

1500 = 2a + 1000 - a

1500 = a + 1000

500 = a

since we now have an exact a and exact c we can find exact b from second statement:

1000 - a = b

1000 - (500) = b

500 = b

therefore to find the equasion, plug the slopes back into the formula y=ax^2 + bx + c.

y = 500x^2 + 500x

y being the amount of money and x being the amount of days, solve for x, when looking for $1,000,000:

1000000 = 500x^2 + 500x

x is approx 44.224154548 days

since you are getting whole thousands each day, we cannot use partial days.

so round down and up and plug in x and solve for y:

y = 500x^2 + 500x

y = 500(44)^2 + 500(44)

y = 990000

y = 500x^2 + 500x

y = 500(45)^2 + 500(45)

y = 1035000

in conclusion, it would take 45 days to have 1 million dollars.