Question

The quadratic function I( t )= - 0.1t2 + 1.6t represents the yearly income (or loss) from a real estate investment, where t is time in years. In what year does income reach its maximum?

Answer 1

8th year

Explanation:

The yearly income or loss of the investment is modeled by a quadratic function. The maximum or minimum value of the quadratic function occurs at its vertex. Since, the coefficient of the squared term is negative, the given function will have a maximum value at its vertex.

The vertex of a quadratic function occurs at =
`(-b)/(2a)`

Here,

a = coefficient of squared term = -0.1

b = coefficient of linear term = 1.6

Using these values, we get:

Vertex occurs at = t =
`(-1.6)/(2(-0.1))=8`

This means, the real estate investment will reach its maximum in 8th year.