Blog 4, Lineal Growth

Part A

Linear Growth
Good Afternoon class, I am unable to attend this lecture on linear growth in person, so I am going to attempt to educate all of you on 'Linear Growth' in this document.  I am first going to describe what it is, I am going to show examples, lastly I am going to give sample problems you can educate yourself and try for yourself on.

What is Linear Growth?
Linear Growth occurs what you have a quantity, that grows by the SAME absolute amount in every unit of time.  In other words (you are getting older every day by the same growth rate of how old you are, so for every 365 days your age goes up by one number.)

Linear growth example
In order to calculate linear Growth, imagine that a graph shows your hight change from the age of 5 years old to 15, making that 10 years of hight growth.  If the graph shows an upwardly sloping line, you are experiencing linear growth.  Calculate the linear growth of your hight the same way you would calculate the slope of the line.  Suppose the x and y coordinates on the graph are (5,4) and (10,5).  This would mean that age of 5, you were 4 feet tall, and age of 10, you were five feet tall. Calculate the rate of linear growth by dividing the difference in height by the difference in time as follows: (5 feet - 4 feet) / 10 years - 5 years) = 1 Foot / 5 Years.

This means that you grew 1 Foot in 5 years.


Example of baby growth rate, in a linear model. 


On the left, this linear model started when the baby was 20 inches in length, wile on the bottem, you have the growth period in days. this is an example of linear growth because the growth rate is the same absolute amount every unit of time.











How to calculate linear growth
- Suppose you are putting a fixed increase in marbles in a bucket every day.

-Choose the amount of marble growth each day = 200
(Hint: choose a whole number for your growth rate, rather than a percent.)

a. Fill in the following chart:

Day (t) Population (p)
t = 0
(1) 100

t = 1
(2) 100 + 200 = 300

t = 2
(3) 100 + 400 = 500

t = 3
(4) 100 + 600 = 700

t = 6
(7) 100 + 1200 = 1300

b) find the linear equation in the form of p = mt + b (y = mx + b), which gives the marble population p,t days from 1.

Answer: p = 200t+100
Explain: using the slope intercept form, with slope=growth rate = 200, intercept = initial population = 100

c) use your equation in part b to approximate the marble population by day 25.

d) use your equation in part b to approximate how many days it would take to reach 7000 marbles in the bucket.