Question

Hi there! Can I get some help please? Thanks!

Answer 1

`p(t) = 0.38t^2-2.45t+5.1`

Explanation:

Let us analyse the differences between consecutive pairs of terms...

Given initial sequence:

`color(blue)(5.1), 3.03, 1.72, 1.17, 1.38, 2.35, 4.08`

The sequence of differences between consecutive terms is:

`color(blue)(-2.07), -1.31, -0.55, 0.21, 0.97, 1.73`

The sequence of differences between those differences is:

`color(blue)(0.76), 0.76, 0.76, 0.76, 0.76`

Having reached a constant sequence, we can use the first term of each of these sequences as coefficients to give us a formula:

`p(t) = color(blue)(5.1)/(0!)+color(blue)(-2.07)/(1!)t+color(blue)(0.76)/(2!)t(t-1)`

`color(white)(p(t)) = 5.1-2.07t+0.38t^2-0.38t`

`color(white)(p(t)) = 0.38t^2-2.45t+5.1`