Maya has saved up some money and decides to take a risk and invest in some stocks. She invests her money in Doogle, a popular computer company. Unfortunately she lost it all over a matter of months. The change in her money during this investment can be represented by the function v(x)=75+72x−3x^2, where v(x) is the value of her investment and x is the time in months.
How many months did Maya's investment last until she lost all her money?
To find the number of months Maya's investment lasted until she lost all her money, we need to solve for x when v(x) = 0.
The equation v(x) = 75 + 72x - 3x^2 can be set to 0:
0 = 75 + 72x - 3x^2
Rearranging the equation:
3x^2 - 72x - 75 = 0
Now we can solve this quadratic equation for x. We can factor out a common factor of 3:
3(x^2 - 24x - 25) = 0
Now we can factor the quadratic equation:
3(x - 25)(x + 1) = 0
Setting each factor to 0:
x - 25 = 0
x = 25
x + 1 = 0
x = -1
Since time cannot be negative, Maya's investment lasted for 25 months until she lost all her money.