Which best describes the graph of the function \( f(x)=4(1.5)^{x} \) ? The graph passes through the point \( (0,4) \), and for each increase of 1 in the \( x \)-values, the \( y \)-values increase by 1.5 . The graph passes through the point \( (0,4) \), and for each increase of 1 in the \( x \)-values, the \( y \)-values increase by a factor of 1.5 . The graph passes through the point \( (0,1.5) \), and for each increase of 1 in the \( x \)-values, the \( y \)-values increase by 4 . The graph passes through the point \( (0,1.5) \), and for each increase of 1 in the \( x \)-values, the \( y \)-values increase by a factor of 4 .

The function \( f(x) = 4(1.5)^x \) is an exponential function. Its graph starts at the point \( (0, 4) \) because when you substitute \( x = 0 \), \( f(0) = 4(1.5)^0 = 4 \). For each increase of 1 in the \( x \)-values, the \( y \)-values increase by a factor of 1.5 due to the base of the exponent being 1.5. This means the graph grows steadily, creating a classic exponential growth curve. In practical terms, you’ll see that as you plot more points on this graph, each time you move one unit to the right along the x-axis, the value of \( f(x) \) will grow by multiplying the previous \( y \)-value by 1.5. So if you started at \( (0, 4) \), moving to \( (1, 6) \) (approximately \( 4 \times 1.5 \)) gives you a clear picture of just how quickly exponential functions can rise, making them a powerful tool in fields like finance or population growth models!