Question

The population of Gatham City is 750. The population can be represented by the equation p(t)=750(1.05)^t, where t is the amount of years from today. If I check the population in 5 years, what would be an appropriate domain to represent this?(3 points)

Answer 1

theres three answers

Answer 2

To determine the appropriate domain for the population model \( p(t) = 750(1.05)^t \) when checking the population in 5 years, we need to consider the variable \( t \), which represents the number of years from today.

Since you are interested in checking the population in 5 years, \( t \) will vary from 0 to 5. Therefore, the appropriate domain for this scenario is:

\[
[0, 5]
\]

This means that \( t \) can take any value from 0 (representing today) to 5 (representing 5 years from now). Thus, the domain is \( t \in [0, 5] \).

Answer 3

Thank you for clarifying! If you're looking for three appropriate answers regarding the domain for the equation \( p(t) = 750(1.05)^t \) for checking the population in Gatham City, here’s how you could present them:

1. **Numerical Interval**: The domain can be expressed as a closed interval, denoting the possible values for \( t \):
\[
[0, 5]
\]

2. **Set Notation**: The domain can also be represented in set notation:
\[
\{ t \in \mathbb{R} \mid 0 \leq t \leq 5 \}
\]
This reads as "the set of all real numbers \( t \) such that \( t \) is between 0 and 5, inclusive."

3. **Descriptive Statement**: A verbal description of the domain could be:
- "The time \( t \) in years from today, where \( t \) can take any value from 0 to 5."

These three components together capture the appropriate domain for the population function as you check it over the next 5 years.