Question
Suppose a city with population 300,000 has been growing at a rate of
years.
The population in 24 years will be approximately
years.
The population in 24 years will be approximately
Ask by Bowers Tyler. in the United States
Jan 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The population of the city in 24 years will be approximately 482,531.
Solution
Given:
- Initial population of the city = 300,000
- Annual growth rate = 2%
To find the population of the city in 24 years, we can use the formula for compound interest:
where:
-
is the final amount (population in 24 years) -
is the initial amount (initial population of 300,000) -
is the annual growth rate (2% or 0.02) -
is the number of years (24)
Substitute the given values into the formula:
Now, we can calculate the population of the city in 24 years.
Calculate the value by following steps:
Calculate the value by following steps:
- step0: Calculate:
- step1: Add the numbers:
- step2: Convert the expressions:
- step3: Simplify:
- step4: Rewrite the expression:
- step5: Rewrite the expression:
- step6: Reduce the numbers:
- step7: Rewrite the expression:
- step8: Rewrite the expression:
- step9: Reduce the numbers:
- step10: Rewrite the expression:
- step11: Rewrite the expression:
- step12: Rewrite the expression:
- step13: Reduce the numbers:
- step14: Multiply the fractions:
The population of the city in 24 years will be approximately 482,531.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To find the population in 24 years, you can use the formula for exponential growth:
where
Calculating it, we have:
Now, calculate
So the population in 24 years will be:
Thus, the population in 24 years will be approximately
Now, to spice things up a bit:
The concept of exponential growth is not just confined to populations; it’s also seen in finance with compound interest. For instance, if you invest $100 at an interest rate of 5% compounded annually, in 24 years, your investment would balloon significantly, demonstrating just how powerful compounding can be.
To avoid any math mistakes while calculating exponential growth, always make sure to double-check your growth factor. It’s easy to confuse the decimal point in growth rates (like 2% vs. 20%) which can lead to wildly inaccurate predictions. Also, remember exponent rules; a little slip here could lead to a big discrepancy down the line!
