The population of Master town was 23,000 in 2012. Assume that Mastertown's population increases at a rate of 2% per year. Write an equation to model the population of Mastertown (y) based on number of years since 2012 (x)

Answer 1

To model the population of Mastertown (y) based on the number of years since 2012 (x), we can use the formula for exponential growth:

\[ y = P_0(1 + r)^x \]

where:

• \(P_0\) is the initial population,
• \(r\) is the growth rate (as a decimal),
• \(x\) is the number of years since the initial population year.

Given:

• The initial population \(P_0 = 23,000\),
• The growth rate \(r = 2% = 0.02\).

Substituting these values into the formula gives us:

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

This simplifies to:

\[ y = 23000(1.02)^x \]

Therefore, the equation to model the population of Mastertown based on the number of years since 2012 is:

\[ y = 23000(1.02)^x \]