Question
A town has a population of 5000 and grows at
be the population after 15 years, to the nearest whole number?
be the population after 15 years, to the nearest whole number?
Ask by Knight Johnson. in the United States
Mar 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The population after 15 years will be approximately 8,377.
Solution
To find the population after 15 years, we can use the formula for compound interest:
where:
-
is the final amount (population after 15 years), -
is the initial amount (population at the start), -
is the annual growth rate (3.5% in this case), -
is the number of years (15 years in this case).
Given:
- Initial population
, - Annual growth rate
, - Number of years
.
Substitute the values into the formula:
Now, we can calculate the population after 15 years using the formula.
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: Reduce the numbers:
- step6: Rewrite the expression:
- step7: Reduce the numbers:
- step8: Multiply the fractions:
The population after 15 years will be approximately 8376.744154. Rounding this to the nearest whole number, the population after 15 years will be approximately 8377.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
The population can be calculated using the formula for exponential growth, which is:
where
Rounding to the nearest whole number, the population after 15 years will be approximately 8569.
To really visualize this population growth, think of it like a snowball rolling down a hill! With every year, that snowball picks up more snow (the town’s population) as it gathers speed (the growth rate). It’s fascinating to see how even a modest growth rate can lead to a significant increase over time, showcasing the power of compound interest in real life!
In real-world scenarios, such calculations are crucial, especially for urban planners and local governments. They need to anticipate the resources and infrastructure required for a growing population. From schools to public transportation, understanding population growth helps to make informed decisions that benefit the community as it expands. Who knew numbers could have such a big impact on shaping our towns?
