Question
- The population of Sacramento is currently 567,345 people. The population has been increasing by
annually.
a) Write the exponential function
b) What will the population be in 10 years? Round your answer to the nearest person.
a) Write the exponential function
b) What will the population be in 10 years? Round your answer to the nearest person.
Ask by Savage Stewart. in the United States
Jan 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
a) The exponential function is
.
b) In 10 years, the population will be approximately 585,180 people.
Solution
To find the exponential function that represents the population of Sacramento, we can use the formula for exponential growth:
where:
-
is the population at time , -
is the initial population, -
is the annual growth rate as a decimal, -
is the time in years.
Given:
- Initial population
people, - Annual growth rate
as a decimal.
a) The exponential function representing the population of Sacramento is:
b) To find the population in 10 years, we substitute
into the function:
Let’s calculate this.
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: Rewrite the expression:
- step7: Reduce the numbers:
- step8: Multiply the fractions:
The population of Sacramento in 10 years will be approximately 585,180 people, rounded to the nearest person.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Mind Expander
To express the population growth, we can use the formula for exponential growth, which is
. Here,
is the initial population (567,345),
is the growth rate (0.0031), and
is the time in years. So, the function would be:
Now, to find the population in 10 years, plug in
:
Calculating this gives approximately:
Thus, the population in 10 years will be around 585,137 people.
If you’re intrigued by how Oakland or San Francisco evolved similarly, explore their population growth trends too! It’s fascinating to look into how urban areas adapt to increasing populations and changing demographics over the decades.
Additionally, consider how this growth impacts local resources, housing, and infrastructure. Cities must plan for population changes to ensure that transportation, schools, and healthcare are adequately supported. A keen eye on these developments can help predict future needs and policy decisions!