Linear & Exponential Population Growth Calculator

Calculates the future populations by using linear, exponential and doubling time population growth model.

  
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Linear Population Growth Formula

Linear Population Growth : A quantitygrows linearly if it grows by a constant amount for each unit of time.

Pt = Po + (k × T)

Where,

Pt is population at time t

Po is population at time zero

k is constant growth rate

T is elapsed time in years from time zero

Exponential Population Growth Formula

Exponential population Growth : A quantity grows exponentially if it grows by a constant factor or rate for each unit of time.

Pt = Po(1 + r/100)T

Where,

Pt is population at time t

Po is population at time zero

T is elapsed time in years from time zero

r is relative growth rate in percentage

Doubling Population Time Growth Formula

Doubling Population time : is the amount of time it takes for a given quantity to double in size or value at a constant growth rate.

Pt = Po (2)tD

Where,

Pt is population at time t

Po is population at initial time

D is the doubling time of a population

t is the amount of time it takes the population to double

Example :

Mr.Bush has inherited a collection of 30 antique frogs. Each year he vows to buy 2 frogs a month to grow the collection.This is an additional 24 frogs per year.How many frogs will he have is six years?

The initial population Po is = 30

The common difference is (t) = 24

The linear growth model for this problem is:

Pt = 30 + 24 . T

The first question asks how many frogs Mr.Bush will have in six years so, T = 6

P6 = 30 + 24 . 6 = 30 + 144 = 174 frogs

Mr. Bush will have 174 frogs in six years.

The above graph of the number of antique frogs Mr.Bush accumulates over time follows a straight line.

Example :

Texas state is growing at a rate of 1.6% per year. The initial population in 2010 is Po = 125000. Calculate the texas population over the next few years.

The relative growth rate is 1.6%. This means an additional 1.6% is added on to 100% of the population that already exists each year. This is a factor of 101.6%

Population in 2011 = 125000 (1.016)1 = 127000

Population in 2012 = 127000(1.016) = 125000(1.016)2 = 129032

Population in 2013 = 129032(1.016) = 125000(1.016)3 = 131097

We can create an equation for the texas state growth. Each year the population is 101.6% more than the previous year.

Pt = 125000(1 + 0.016)t

Texas population over the next 3 years is 131097

The above graph of the texas growth follows an exponential growth model.

Example :

The doubling time of a population of flies is 8 days. If there are initially 100 flies, how many flies will there be in 17 days?

To solve this problem, use the doubling time model with D = 8 and Po

Pt = 100 . (2)t8

When t = 17 days,

P17 = 100 . (2)178 = 436

There are 436 flies after 17 days.

The above graph of the flies growth follows an doubling time growth model.

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