Question

Please help with #27 and please explain

Answer 1

(a) 3 added to twice the value of n

(b)
`T = 2n +3`

Explanation:

Given

Table #27

Solving (a): First, we express as an equation

The table illustrates a linear function; so, we calculate the slope (m) first

`m = (T_2 - T_1)/(n_2 -n_1)`

Where:

`(n_1.T_1) = (4,11)`

`(n_2.T_2) = (8,19)`

So:

`m = (T_2 - T_1)/(n_2 -n_1)`

`m = (19 - 11)/(8-4)`

`m = (8)/(4)`

`m = 2`

The equation is then calculated using:

`T = m(n - n_1) + T_1`

`T = 2(n - 4) + 11`

`T = 2n - 8 + 11`

`T = 2n +3`

In words, the equation is: 3 added to twice the value of n

Solving (b): As an equation.

This has been solved in (a) above:

`T = 2n +3`