To determine which equation is modeled by the graph you described, we need to consider the characteristics of the curve in terms of exponential growth or decay.
Given the options:
- \( y = -3.5(4)^x \)
- \( y = 10(4)^x \)
- \( y = 3.5(4)^x \)
- \( y = 50(4)^x \)
The presence of positive values suggests exponential growth, as negative coefficients would make the graph reflect downwards, which is not typical for growth functions.
When examining growth functions with the base of 4, we can infer the following:
- If the value of \( x \) increases (moving right on the x-axis), \( y \) also increases rapidly when multiplied by a positive coefficient (like 10, 3.5, or 50).
Without the specific graph, we typically see that functions \( y = 10(4)^x \), \( y = 3.5(4)^x \), and \( y = 50(4)^x \) will all increase as \( x \) increases. However, different coefficients will result in different rates of growth:
- \( y = 10(4)^x \) grows more slowly than \( y = 50(4)^x \), for example.
If you can observe the initial values or overall steepness of the curve, you can decide which coefficient seems the most appropriate.
Since I cannot see the graph, you would typically select the option that matches the steepness and starting points shown.
For example, if the graph starts relatively low and grows quickly, then \( y = 10(4)^x \) or \( y = 3.5(4)^x \) might be suitable. If it starts much higher, then \( y = 50(4)^x \) would be more appropriate.
Given I'm unable to view the specific details and based on typical behaviors, I highly suggest you evaluate the initial conditions and growth rates as displayed in the graph and choose the option that fits best.