the population of mastertown was 23,000 in 2012. assume that mastertowns population increases at a rate of 2% per year. write an

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SCORPION-xisa

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the population of mastertown was 23,000 in 2012. assume that mastertowns population increases at a rate of 2% per year. write an

equation to model the population of mastertown (y) based on numbers of years since 2012 (x)

Mathematics

2 answers:

babunello [11.8K] · Answer 1 · 2026-04-04T08:45:51+03:00

The population of Mastertown is 23,000 in 2012.
Assuming a yearly increase of 2%, we can model future population with an exponential growth formula. Using the geometric sequence form gives:

A_n = A_1 * r^(n-1)

<span>Population = initial population in 2012 × 0.02^[(year - 2012) - 1]</span>

Inessa [12.5K] · Answer 2 · 2026-04-04T08:46:18+03:00

Answer: y = 23000 (1 + 0.02)^x

Step-by-step solution:

The population in 2012 is 23,000

The annual growth rate is 2%

Using the compound growth formula:

y = a(1 + r)^n

a = initial value

n = number of years

r = growth rate

Interpreting for population (y) after x years since 2012:

a = 23000

Growth rate 2%

r = 2/100 = 0.02

So the model is:

y = 23000 (1 + 0.02)^x