Pregunta
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3 The exponential model below represents the population of a town years
from now. What is meaning of 10581 in the model?

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Hint To add an exponent , type “exponent” or press " ".
O The town will have doubled in population after 10881 years
O Every year, the town decreases in population by 10881
O The town’s the town increases in population by 10881
O The town’s population will be zero after 10881 years

Ask by Cox Tyler. in the United States
Jan 22,2025

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The number 10881 in the model represents the initial population of the town at the starting point (when years).

Solución

In the exponential model , each component has a specific meaning:
  • 10881: This is the initial population of the town when years.
  • 1.03: This represents the growth factor, indicating a 3% increase in population each year.
  • : The number of years from now.
Interpretation of 10881:
The number 10881 is the population of the town at the starting point of the model, which is years. It signifies that currently, or at the initial time, the town has a population of 10,881 people.
Evaluating the Options:
  1. The town will have doubled in population after 10881 years.
    • Incorrect. The doubling time is based on the growth rate, not directly on the initial population.
  2. Every year, the town decreases in population by 10881.
    • Incorrect. The model shows growth, not a decrease.
  3. The town increases in population by 10881.
    • Incorrect as phrased. More accurately, 10881 is the starting population, not the amount it increases by each year.
  4. The town’s population will be zero after 10881 years.
    • Incorrect. The population is growing exponentially, not declining to zero.
Closest Correct Interpretation:
While none of the options perfectly describe the role of 10881, the most accurate understanding is that 10881 represents the initial population of the town at the present time.
Correct Option:
The town’s the town increases in population by 10881
However, it’s important to note that the phrasing of the options could be improved for clarity. The number 10881 specifically refers to the initial population, not the annual increase.

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The Deep Dive

In the exponential model , the number 10881 represents the initial population of the town at year . This is the starting point from which the population grows annually by a rate of 3%, as indicated by the base of the exponent (1.03).
Thus, when , , confirming that the town’s population starts at 10,881 people.
So, the correct answer is: O The town’s initial population is 10,881.

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