Question

Earn $1700 as a starting bonus (at day zero) and then earn $5,000 after your first month, $6,000 after your

second month, $7,000 after your third month, etc.

Write the explicit formula

Answer 1

`n(t) =5700+ 1000t`;
`t > 0`

`n(t) = 1700`;
`t =0`

Explanation:

Given

`n(0) = 1700` --- initial

`n(1) = 5000`

`n(2) = 6000`

`n(3) = 7000`

Required

Explicit formula

First, we calculate the difference between the earnings of successive months.

`d = n(2) - n(1) = n(3) - n(2)`

So, we have:

`d = 6000 - 5000`

`d = 1000`

The explicit formula is:

`n(t) = n(0) + n(1) + (t - 1)d`

Where

`t \to` months

`n(t) = 1700 + 5000 + (t - 1) * 1000`

Open bracket

`n(t) = 1700 + 5000 + 1000t - 1000`

Collect like terms

`n(t) = 1700 + 5000 - 1000+ 1000t`

`n(t) =5700+ 1000t`