Question

the population of mastertown was 23,000 in 2012. assume that mastertowns population increased at a rate of 2% per year. write an equation to model the population of mastertown (y) based on a number of years since 2012(x).

Answer 1

Answer:

An equation to model the population of mastertown (y) based on a number of years since 2012(x) is $y=23000(1+0.02)^x$

Step-by-step explanation:

Given : The population of mastertown was 23,000 in 2012. assume that mastertowns population increased at a rate of 2% per year.

To find : write an equation to model the population of mastertown (y) based on a number of years since 2012(x).

Solution :

There is an exponential growth :

The equation for the growth of the population is given by:

$y=a(1+r)^x$

where

a is the initial amount,

x is the number of years,

r represents the growth rate( in decimal)

y represents the population of Master-town based on number of years.

According to question,

The population of mastertown was 23,000 in 2012.

i.e, a= 23000

Mastertowns population increased at a rate of 2% per year.

r=2%=0.02

Substitute in function we get,

$y=23000(1+0.02)^x$

An equation to model the population of mastertown (y) based on a number of years since 2012(x) is $y=23000(1+0.02)^x$

Answer 2

Exponential growth is

F=P(1+r)^t
F=future amount
P=present amount
r=rate
t=time in years

rate=2%=0.02
therefor the equation is
f(x)=23,000(1+0.02)^x
f(x)=23,000(1.02)^x
where x=time in years from 2012