The value, V< of Juan's investment portfolio can be modeled by the equation V=16t^2-256t+16,000. When will Juan's investment portfolio be worth $16.576.00?
I think you wrote the last number wrong
but, making a reasonable assumption, just solve
16t^2+256t+16000 = 16576
t = 2
To find when Juan's investment portfolio will be worth $16,576.00, we need to set the equation equal to $16,576.00 and solve for t.
The equation is: V = 16t^2 - 256t + 16,000
We set it equal to $16,576.00: 16,576.00 = 16t^2 - 256t + 16,000
This creates a quadratic equation that we can solve by using the quadratic formula:
The quadratic formula is: t = (-b ± √(b^2 - 4ac)) / (2a)
Comparing the equation to the standard quadratic form ax^2 + bx + c = 0, we can assign values:
a = 16, b = -256, c = 16,000
Substituting these values into the formula, we get:
t = (-(-256) ± √((-256)^2 - 4(16)(16,000))) / (2(16))
Simplifying further:
t = (256 ± √(65,536 - 10,240)) / 32
t = (256 ± √55,296) / 32
t = (256 ± 234.91) / 32
So we have two possible solutions:
t = (256 + 234.91) / 32
t = 490.91 / 32
t ≈ 15.34
t = (256 - 234.91) / 32
t = 21.09 / 32
t ≈ 0.66
Therefore, Juan's investment portfolio will be worth $16,576.00 approximately in 15.34 years or 0.66 years.