a town has a population of $1.303 \\times 10^5$ and grows at a rate of 5.5% every year. which equation…
a town has a population of $1.303 \\times 10^5$ and grows at a rate of 5.5% every year. which equation represents the town’s population after 2 years?
Answer
Explanation:
Step1: Recall the exponential growth formula
The formula for exponential growth is ( P(t)=P_0(1 + r)^t ), where ( P_0 ) is the initial population, ( r ) is the annual growth rate (as a decimal), and ( t ) is the time in years.
Step2: Identify the values
Here, ( P_0 = 1.303\times10^{5} ), ( r = 5.5%=0.055 ), and ( t = 2 ).
Step3: Substitute the values into the formula
Substituting these values into the formula, we get ( P(2)=1.303\times10^{5}(1 + 0.055)^{2} ), which simplifies to ( P(2)=1.303\times10^{5}(1.055)^{2} ).