the initial population of a small town was 2.53 thousand. the population grows at a rate of 2.15% each year…

the initial population of a small town was 2.53 thousand. the population grows at a rate of 2.15% each year. after how many years will the population have doubled?

the initial population of a small town was 2.53 thousand. the population grows at a rate of 2.15% each year. after how many years will the population have doubled?

Answer

Answer:

Approximately 32.4 years

Explanation:

Step1: Define growth formula

The exponential growth formula is $P(t) = P_0(1 + r)^t$, where $P_0=2.53$, $r=0.0215$, and $P(t)=2P_0$.

Step2: Set up doubling equation

Substitute values: $2P_0 = P_0(1 + 0.0215)^t$ Cancel $P_0$: $2 = (1.0215)^t$

Step3: Solve for t using logs

Take natural log of both sides: $\ln(2) = t\ln(1.0215)$ Rearrange to solve for t: $t = \frac{\ln(2)}{\ln(1.0215)}$

Step4: Calculate the value

Compute: $t = \frac{0.6931}{0.0213} \approx 32.4$