If the population of a city is 135,000.  If the population declines continuously by 5​% per​ year, what will the population be in 15 ​years?
The population will be enter your response here.
If​ necessary, round to the nearest integer.

To find the population after 15 years with continuous decline, we can use the formula for continuous exponential decay:

\[
P(t) = P_0 \times e^{rt}
\]

Where:
- \( P(t) \) is the population after time \( t \).
- \( P_0 \) is the initial population.
- \( r \) is the rate of decline (negative for a decline).
- \( t \) is the time in years.
- \( e \) is the base of the natural logarithm (approximately 2.71828).

Given:
- \( P_0 = 135,000 \)
- \( r = -0.05 \) (since it's a 5% decline per year)
- \( t = 15 \) years

Now we can plug in the values:

\[
P(15) = 135,000 \times e^{-0.05 \times 15}
\]

Let's calculate this.The population of the city after 15 years will be approximately **63,769**.

Would you like further details or have any questions? 

Here are some related questions you might find interesting:

1. How would the population change if the decline rate were 3% instead of 5%?
2. What would be the population after 10 years with the same decline rate?
3. How does the formula for continuous exponential decay differ from that of discrete decay?
4. What is the population after 20 years with a 5% decline rate?
5. How does the choice of rounding affect the interpretation of population statistics?

**Tip:** Continuous decay formulas are very useful for modeling processes where change happens at every instant, like population decline or radioactive decay.

If the population of a city is 135,000 and it declines continuously by 5% per year, what will the population be in 15 years? Round to the nearest integer if necessary.

Learn how to calculate the population decline of a city over 15 years with a continuous 5% annual decrease. Understand key concepts like exponential decay, continuous compounding, and apply the exponential decay formula. Suitable for high school students in Grades 9-12.

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