how do i solve this and what is the answer?

This is an exponential decay graph, so the value of b is going to be less than 1 but greater than 0. Let's look at some coordinates on this graph to easily find "b":

(-2,4),(-1,2),(0,1),(1,0.5)

As you can see, we get from one y value in a coordinate to the next y value in the coordinate next to it by dividing by 2. Therefore, the value of b is 1/2.

Answer Link

zarahaider4211 zarahaider4211 · Answer 2 · 2024-06-16T19:07:58-04:00

Answer:

b = 0.5 or 1/2

Step-by-step explanation:

Interpreting a Graph

For an equation or function, a line can be drawn that shows the possible x-values that can be plugged in and, its correlating y-values.

For any coordinate point on a line, the x-value is a possible "input" value into the function/equation and the y-value is the "output" that the function/equation evaluates to.

Solving the Problem

On the graph we're shown the point (-1,2). This means that when x = -1, the y-value should equal to 2 or,

[tex]2=b^-^1[/tex].

Using the exponent property of [tex]a^-^c=\dfrac{1}{a^c}[/tex], for some base a and some integer exponent c, the right side of the equation simplifies to,

[tex]2=\dfrac{1}{b}[/tex].

Now we rearrange to find the value of b!

[tex]2b=1[/tex]

[tex]b=\dfrac{1}{2}[/tex]