Question

The function f(x)=3(1.25)x represents the population growth of a swarm of fruit flies. Create a graph modeling the equation, and determine which graph models the situation accurately.

(1 point)
Responses

Option #2
Option #2

Option #4
Option #4

Option #3
Option #3

Option #1

Answer 1

To determine which graph accurately models the population growth function \( f(x) = 3(1.25)^x \), we can consider a few key characteristics of exponential growth:

1. **Initial Value**: At \( x = 0 \), the population \( f(0) = 3(1.25)^0 = 3 \).
2. **Growth Rate**: The population grows by a factor of 1.25 for every increase of 1 in \( x \).
3. **Behavior as \( x \) increases**: The graph will rise steeply as \( x \) becomes larger due to the exponential growth.

Now, if we had the actual graphs available, we would look for a graph that starts at 3 when \( x = 0 \) and increases exponentially, getting steeper as \( x \) increases.

Without visual options, I cannot directly pick a suitable option from those provided, but here’s how you can analyze them:

- **Look for the starting point**: It should intersect the y-axis at 3.
- **Check the growth shape**: It should curve upwards, becoming steeper as \( x \) increases.
- **Growth Factor**: The slope of the graph should reflect the 25% increase per unit increase in \( x \).

Choose the graph that matches these criteria!