Use the rule for term n of a linear growth or decay model

A value starts at V₀. How many yearly changes are included in V₄?

Start with a yearly change of $200. Move the years to 5. Then use −$200 and zero to compare growth, decay and no change

At year 4 with a yearly change of −$200, what is the value?

Add a signed change

Add a signed change for each period, or subtract a positive loss for each period. Do not subtract a negative loss twice

1. 1Growth D is positive
2. 2Decay D is negative in the signed-change rule
3. 3Index n counts the equal periods or usage blocks stated in the question

Given values

\(\displaystyle \text{Yearly loss}=200\)

An asset loses $200 per year. What is its signed yearly change?

Given values

\(\displaystyle V_0=3000,\quad D=-200\)

Starting at $3,000 with yearly change −$200, find V₄

Given values

\(\displaystyle V_0=3000,\quad V_4=2200\)

How much value was lost over those four years?

Given values

\(\displaystyle P=5000,\quad r=3\)

A $5,000 investment earns 3% simple interest yearly. Find its yearly change

Given values

\(\displaystyle V_0=5000,\quad D=150\)

An investment starts at $5,000 and gains $150 per year. Find its balance after six years

Given values

\(\displaystyle V_0=8000,\quad D=-60\)

An asset starts at $8,000 and loses $60 per 100 hours. Find its value after five of those blocks

Check the start and direction

At n = 0, the explicit rule must return the starting value. Increasing n should raise a growth model and lower a depreciation model

1. 1Independent rule writing Here n is the number of 100-hour blocks. Have your explanation checked separately from numeric practice \(\displaystyle V_n=8000-60n\)