Question

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

Answer 1

Answer:

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

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

Step-by-step 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

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

$n(t) =5700+ 1000t$