Question

The answer should be accurate to at least 2 decimal places.

Answer 1

`\boxed{20}`

Explanation:

For instantaneous rate of change, we can use differentiation and differentiate 'g' wrt 't'.

Given,

`g(t) = 5 {t}^(2) - 1`

According to power constant rule; d(ax^n)/dx = n*ax^(n-1). And differentiation of a constant is 0.

Differentiating 'g' wrt 't'

`(d \: g(t))/(dt) = 10t`

Instantaneous rate of change at t = 2,

`(d \: g(2))/(dt) = 10(2) = 20`

The instantaneous rate of change of g (5t² - 1) is 20.