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.

Question

How many months did Maya's investment last until she lost all her money?

Answer 1

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.