Question

A small mass of wasp has an exponential growth rate of 13% per month if the nest currently has 5,000 walls the situation can be modeled by the equation w of w x t equals 5000 * 1.13 t where w is the number of wasp and t for month which of the following statement is true about the equation
The domain t values can be all real numbers the range w values include the values greater than 0 and less than or equal to 5,000 the domain t values includes the values of t such as t is great is greater than or less than 0

Answer 1

Let's analyze the given exponential growth model for the wasp population. The equation is:

\[ w(t) = 5000 \times 1.13^t \]

where:
- \( w(t) \) is the number of wasps at time \( t \) (in months),
- \( t \) is the time in months,
- The equation represents a population that grows exponentially at a rate of 13% per month.

Now, let's evaluate the statements one by one:

1. **The domain \( t \) values can be all real numbers.**
- This statement is **false**. The variable \( t \) (time in months) must be non-negative in the context of this growth model, so \( t \) can only take values \( t \geq 0 \).

2. **The range \( w \) values include the values greater than 0 and less than or equal to 5,000.**
- This statement is **false**. Since the population is growing exponentially from a starting value of 5,000, the number of wasps can become greater than 5,000 as time progresses. The range of \( w \) would be from \( 5000 \) to \( \infty \) (i.e., \( w > 5000 \) for \( t > 0 \)).

3. **The domain \( t \) values include the values of \( t \) such as \( t \) is greater than or less than 0.**
- This statement is **false**. As previously mentioned, \( t \) must be non-negative: \( t \geq 0 \). Therefore, it cannot include values less than 0.

In conclusion, none of the statements provided about the equation are true. The correct domain for \( t \) is \( t \geq 0 \), and the range for \( w \) begins at \( 5000 \) and extends to \( \infty \).