Using the concept of exponential growth and exponential decay. Solve

Seamus Kent

Seamus Kent

Answered question

2022-02-01

Using the concept of exponential growth and exponential decay. Solve the given problem.
1. A small locality has a population of 52,365 in 2012. If its population increases 3% every 2 years,
a. Derive a function P that determines the population t years after 2012.
b. What is the expected population in 2020?

Answer & Explanation

Rohan Mercado

Rohan Mercado

Beginner2022-02-02Added 10 answers

Exponential equation of the form
P(x)=abx Where P(x) represents the population after x years and ‘a’ represents the initial population
‘b’ is the growth/decay factor
X represents the number of years
A small locality has a population of 52,365 in 2012. If its population increases 3% every 2 years
Initial population is 52365
After 2 years , that is at x=2 the population increases by 3%
Find out 3% of 52365
3100×52365=1570.95
After 2 years the population becomes 52365 + 1570.95 = 53935.95
We use the exponential equation
we know that initial population is 52365
After 2 years the population becomes 53935.95
P(x)=abx
a=52365
When, x=2,P(x)=53935.95
53935.95=52365(b)2
53935.9552365=b2
53935.95523652=b
b=1.015
The exponential function P that determines the population t years after 2012.
We use ‘t’ instead of x
P(x)=abx
P(t)=52365(1.015)t
Now we find the expected population in 2020
Initial year is 2012, the number of years between 2020 and 2012 is 8 years
We need to find the population after 8 years. So we plug in 8 for t
P(t)=52365(1015)t
P(8)=52365(1015)8
P(8)=58988.78(
58,988 is the expected population in 2020

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