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