Pregunta
A town has a population of 12000 and grows at
will be the population after 7 years, to the nearest whole number?
will be the population after 7 years, to the nearest whole number?
Ask by Pope Chambers. in the United States
Mar 21,2025
Solución de inteligencia artificial de Upstudy
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After 7 years, the population will be approximately 15,267.
Solución
To find the population after 7 years, we can use the formula for exponential growth:
where:
-
is the population after years, -
is the initial population, -
is the annual growth rate, -
is the number of years.
Given:
- Initial population
, - Annual growth rate
, - Number of years
.
Substitute the values into the formula:
Now, we can calculate the population after 7 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: Rewrite the expression:
- step8: Reduce the numbers:
- step9: Multiply the fractions:
The population after 7 years will be approximately 15267.351153. Rounding this to the nearest whole number, the population after 7 years will be approximately 15267.
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Simplifique esta solución The Deep Dive
To find the future population, we can use the formula for exponential growth:
Where:
-
is the future population, -
is the current population (12,000), -
is the growth rate (0.035), -
is the number of years (7).
Plugging in the values, we get:
Thus, the population after 7 years will be approximately 15,509 people when rounded to the nearest whole number.
Over the years, many towns have used similar mathematical models to project growth, helping them prepare for changes in resources, infrastructure, and needs of the community. Population growth projections are crucial for urban planning and resource allocation, enabling town leaders to create sustainable future plans.
In practical situations, it’s vital to consider factors like migration and local policies that might impact population growth, alongside just natural increase rates. Additionally, when doing such calculations, it’s common to overlook rounding at early steps; ensure to keep decimals until the final answer is calculated for more accuracy!
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