Determine when the Population will Reach 71 Million using the Exponential Model MyMathlab

TL;DR

Use exponential model to find population growth year.

Transcript

the exponential model a I'm gonna write it out a equals 55.4 e to the zero point zero one two t describes the population a of a country in millions T years after 2003 okay so this is the population of the country T years after 2003 it says use the model to determine when the population of the country will be 71 million okay so this is the populatio... Read More

Key Insights

• ⌛ Exponential models are used to describe population growth over time.
• 😫 Setting the model equal to a specific population value allows the determination of the corresponding time.
• ⌛ Natural logarithms are employed to isolate the time variable in exponential equations.
• ❓ Calculations involving exponential growth can be accurately determined using logarithmic functions.
• 🦻 Understanding exponential models aids in predicting future population sizes.
• 😒 The use of rounding values may be necessary to provide practical solutions.
• 🖐️ Mathematical concepts like the natural logarithm play a vital role in solving real-world problems.

Questions & Answers

Q: How does the exponential model describe population growth?

The exponential model, represented as a=55.4e^0.012t, shows how the population of a country changes over time T years after 2003.

Q: What is the significance of setting the model equal to 71 million?

Setting the model a=55.4e^0.012t equal to 71 million allows us to find the time T when the population of the country reaches that specific value.

Q: What role do natural logarithms play in solving for T?

By taking the natural logarithm of both sides of the equation, we can isolate T and calculate the exact number of years required for the population to reach 71 million.

Q: How is the final year of reaching 71 million population calculated?

By adding the calculated T value of 21 years to the base year of 2003, we get the result that the population will reach 71 million in the year 2024.

Summary & Key Takeaways

• The exponential model describes the population of a country in millions T years after 2003.

• To determine when the population will be 71 million, set the model equal to 71 and solve for T.

• By calculating with natural logarithms, the result shows the population will reach 71 million in the year 2024.