The value of jennifer's stock portfolio (in dollars) is given by the function f(t) = -3t +72t + 5000, where t is the time in months since she opened the account. after how many months will her portfolio be at a maximum? what is the maximum value of the portfolio?

a) The portfolio will be at maximum after 12 months (1 year)

b) The maximum value of the portfolio is $5432

Step-by-step explanation:

The function that models Jennifer's stock portfolio (in dollars) is , where t is the time in months since she opened the account.

We complete the square to obtain this function in vertex form:

Factor -3 from the first two terms

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Add the zero pairs -3(+144),-3(-144)

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Factor the perfect square trinomial and simplify.

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The vertex of this function is (h,k)=(12,5432)

a) The portfolio will be at maximum when t=12, the h-value of the vertex

b) The maximum value of the portfolio is the k-value of the vertex which is 5432