Question

the scatterplot shows the relationship between two variables, x and y. an equation for the exponential model shown can be written as y = a(b)^x, where a and b are positive constants. which of the following is closest to the value of b? a. 0.84 b. 1.84 c. 1.74 d. 1.94

Explanation:

Step1: Identify key - point of exponential function

The general form of the exponential function is \(y = a(b)^{x}\). When \(x = 0\), \(y=a(b)^{0}=a\). Looking at the graph, when \(x = 0\), \(y\approx1\), so \(a\approx1\).

Step2: Choose a non - zero point

Let's take the point \((1,1.84)\) (approximate value from the graph). Substitute \(x = 1\), \(y=1.84\) and \(a = 1\) into \(y=a(b)^{x}\). We get \(y=(1)(b)^{1}\), so \(b=y\) when \(x = 1\).

Step3: Determine the value of \(b\)

Since when \(x = 1\), \(y\approx1.84\), then \(b\approx1.84\).

Answer:

b. 1.84