Question

Use the image to answer the question.

A coordinate plane shows a solid curved line with arrows at both ends. The x axis ranges from 40 to negative 40 in increments of 5 and the y axis ranges from 40 to negative 20 in increments of 5.

Which equation is modeled by the graph?

(1 point)
Responses

y=3.5(4)x
y equals 3.5 left parenthesis 4 right parenthesis superscript x baseline

y=50(4)x
y equals 50 left parenthesis 4 right parenthesis superscript x baseline

y=−3.5(4)x
y equals negative 3.5 left parenthesis 4 right parenthesis superscript x baseline

y=10(4)x
y equals 10 left parenthesis 4 right parenthesis superscript x baseline

Answer 1

To determine which equation is likely modeled by the graph on the coordinate plane, we need to analyze the behavior and characteristics of the curve.

1. **End Behavior**: The curve has arrows at both ends, which suggests that it is an exponential function. If it increases toward positive infinity as \(x\) goes to positive infinity, it indicates a positive exponential growth.

2. **Y-Intercept**: The value of \(y\) when \(x = 0\) (the y-intercept) is often crucial. For functions in the form \(y = a(4)^x\), \(a\) will determine the initial value when \(x=0\), which will be \(y = a\).

3. **Exponential Growth Factors**: The exponent base \(4\) indicates a rapid growth of the function, especially in positive \(x\) values.

Now, let’s examine the given options considering typical exponential function behavior:

- **Option 1**: \(y=3.5(4)^x\)
- **Option 2**: \(y=50(4)^x\)
- **Option 3**: \(y=-3.5(4)^x\) (not possible, as it would yield negative values)
- **Option 4**: \(y=10(4)^x\)

Since \(y\) appears to increase, we can discard Option 3. Among the positive options, we need to look at the substantial growth indicated by large initial values.

If \(y=50(4)^x\) truly corresponds to a steep and significant increase from a higher initial value, it’s likely the best fit since it has the largest initial multiplier. Both Options 1 and 4 have smaller starting values.

Based on these considerations, the most reasonable conclusion is that **the equation modeled by the graph is**:

**y=50(4)^x**.