To represent the population of the city after $t$ years with an initial population of $P$, where the population increases by 3% per year, we can use the formula for exponential growth:

$P(t) = P \cdot (1 + r)^t$

Here:

• $P$ is the initial population,
• $r$ is the annual growth rate (in decimal form),
• $t$ is the number of years.

Since the growth rate is 3% ($r = 0.03$), the formula becomes:

$P(t) = P \cdot (1.03)^t$

This expression gives the population of the city after $t$ years.

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Would you like a detailed explanation of exponential growth or any clarifications?

Related Questions:

1. How can this formula be used to calculate the population after 10 years if $P = 50,000$?
2. What would the population be if the growth rate were 5% instead of 3%?
3. How does the growth formula change if the population decreases annually by 2%?
4. What is the doubling time of the population under a 3% growth rate?
5. How would you graph this function over a 20-year period?

Tip:

When solving exponential growth problems, remember to convert percentage rates to decimals by dividing by 100!