Question

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one of the digits in your answer is wrong. check your work carefully.
a city has a population of 380,000 people. suppose that each year the population grows by 5.25%. what will the population be after 10 years?
use the calculator provided and round your answer to the nearest whole number.
633878 people

Explanation:

Step1: Recall the population growth formula

The formula for exponential population growth is $P = P_0(1 + r)^t$, where $P_0$ is the initial population, $r$ is the annual growth rate (in decimal), and $t$ is the time in years.
Here, $P_0 = 380000$, $r = 5.25\% = 0.0525$, and $t = 10$.

Step2: Substitute the values into the formula

Substitute the values into the formula: $P = 380000\times(1 + 0.0525)^{10}$.
First, calculate $(1 + 0.0525) = 1.0525$. Then, calculate $1.0525^{10}$. Using a calculator, $1.0525^{10}\approx1.6674$.

Step3: Calculate the final population

Multiply the initial population by the growth factor: $P = 380000\times1.6674 = 633612$. (Rounded to the nearest whole number)

Answer:

633612