somerville has a population of 38,400 people. the town has been seeing its population decline by 3% every…

somerville has a population of 38,400 people. the town has been seeing its population decline by 3% every year. if this trend continues, what will the population be in 3 years? if necessary, round your answer to the nearest whole number. people

somerville has a population of 38,400 people. the town has been seeing its population decline by 3% every year. if this trend continues, what will the population be in 3 years? if necessary, round your answer to the nearest whole number. people

Answer

Explanation:

Step1: Identify the formula

The formula for exponential decay is $A = P(1 - r)^t$, where $P$ is the initial amount, $r$ is the rate of decay as a decimal, and $t$ is the time. Here, $P = 38400$, $r=0.03$, and $t = 3$.

Step2: Substitute the values

$A=38400\times(1 - 0.03)^3=38400\times(0.97)^3$.

Step3: Calculate $(0.97)^3$

$(0.97)^3=0.97\times0.97\times0.97 = 0.912673$.

Step4: Calculate $A$

$A = 38400\times0.912673=35046.6432$.

Step5: Round the result

Rounding $35046.6432$ to the nearest whole - number gives $35047$.

Answer:

35047