the scatterplot shows the relationship between two variables, x and y. an equation for the exponential model…
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
Answer
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