Question

An economist uses the model P (x) = minus−0.05xsuperscript3end of superscript, + 3.25xsuperscript2end of superscript, - 10x + 20 to estimate the price of a stock over the next 8 years.

When does the stock reach at least $52.56?
Enter a whole number of years. (Hint: An answer of 6.23 years refers to being in the seventh year.)

Answer 1

To find when the stock reaches at least $52.56, we need to set the equation P(x) equal to $52.56 and solve for x.

Given:
P(x) = -0.05x^3 + 3.25x^2 - 10x + 20
P(x) = $52.56

Setting the equation equal to $52.56:

-0.05x^3 + 3.25x^2 - 10x + 20 = $52.56

Rearranging the equation:

-0.05x^3 + 3.25x^2 - 10x + 20 - $52.56 = 0

Combining like terms:

-0.05x^3 + 3.25x^2 - 10x - $32.56 = 0

To find the solution(s), we can use numerical methods or graphing software. By solving this equation, 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 (as a whole number of years).

Answer 2

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.