Question

According to a psychologist, the ability of a person to understand spatial concepts is given by `A = 1/3sqrtt`, where t is the age in years, t ∈ [5, 18]. Show that the rate of increase of the ability to understand spatial concepts decreases with age in between 5 and 18.

Answer 1

`A = 1/3sqrtt`

`therefore (dA)/dt = 1/6t^(-1/2) = 1/(6sqrtt); forallt in (5, 18)`

`(dA)/dt = 1/(6sqrtt)`

`therefore (d^2A)/(dt^2) = -1/(12tsqrtt)`

So, `(d^2A)/dt^2 < 0, forallt in (5, 18)`

This means that the rate of change of the ability to understand spatial concepts decreases (slows down) with age.