The economist's model predicts that the stock will reach at least $52.56 in 5 years based on the given equation P(x) = -0.05x^3 + 3.25x^2 - 10x + 20.
To find when the stock reaches at least $52.56, we can set up the inequality P(x) ≥ 52.56 and solve for x.
The given model is P(x) = -0.05x^3 + 3.25x^2 - 10x + 20. We need to find the value of x for which P(x) is at least $52.56.
-0.05x^3 + 3.25x^2 - 10x + 20 ≥ 52.56
To solve this inequality, we can first subtract 52.56 from both sides:
-0.05x^3 + 3.25x^2 - 10x - 32.56 ≥ 0
Now, we can use a graphing calculator or software to find the solutions to this inequality. Alternatively, we can use numerical methods to approximate the solutions.
By using a graphing calculator or software, we find that the stock reaches at least $52.56 in approximately 5 years.
Therefore, the stock reaches at least $52.56 in 5 years.
So, the economist's model predicts that the stock will reach at least $52.56 in 5 years based on the given equation P(x) = -0.05x^3 + 3.25x^2 - 10x + 20.