Question

A painting originally sold for $1500increases rapidly in value. A year after being sold, the painting is worth $2550, and a year after that, it is valued at $4335. The artist wants to figure out a function for the value of the painting if it continues to increase in the same manner.

Answer 1

Explanation:

Let V(t) be the value of the painting t years after it was originally sold. Then, we have:

V(0) = $1500 (since the painting was originally sold for $1500)

V(1) = $2550 (since the painting was worth $2550 one year after being sold)

V(2) = $4335 (since the painting was valued at $4335 two years after being sold)

We can use these values to find a quadratic function for V(t) of the form:

V(t) = at^2+ bt + c

where a, b, and c are constants to be determined.

Substitute,

a(0)^2 + b(0) + c = $1500 a(1)^2 + b(1) + c = $2550 a(2)^2 + b(2) + c = $4335

Simplify,

c = $1500 a + b + c = $2550 4a + 2b + c = $4335

Solving these equations simultaneously, we get:

a = $925/2 b = $675/2

so, the function for the value of the painting if it continues to increase in the same manner is:

V(t) = ($925/2)t^2 + ($675/2)t + $1500