Question

Who can answer this?

Answer 1

Notice that the graph is decreasing as x increases, showing exponential decay. An exponential decay graph is in the form
`y = ab^x`, where a is just multiplying
`b^x` and b < 1. That means the value of b we are looking for is less than 1. This isn't crucial information, but it's nice to know!

Also remember the negative exponent rule says that when a base has a negative exponent, flip the base onto the other side of the fraction to make it into a positive exponent. For example,
`b^(-2) = (1)/(b^(2) )`.

Back to the Problem
Let's pick out an easy value on the graph. I went with (-1, 2). Since we know the equation is
`y = b^x`, plug the coordinate in and solve for b:

`y = b^x\\ 2 = b^(-1)\\ 2 = (1)/(b) \\ 2b = ( (1)/(b))b\\ 2b = 1\\ b = (1)/(2)`

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Answer:
b =
`(1)/(2)`

Answer 2

Remark.
All you need to do to solve this is to pick one point that's clear on the graph. I'd like to be able to pick something where x > 0 but I cannot. It's too hard to read the y value. One point that is very clear is (-2, 4)

Substitute and Solve.
y = b^x
Let x = - 2
Let y = 4

4 = b^(-2) Put b in the denominator so that you have a positive power. Also put a 1 underneath the 4


`(4)/(1)=(1)/(b^2)` Cross multiply
4b^2 = 1 Divide by 4
b^2 = 1/4 Take the square root of both sides.
b = +/- 1/2

Answer: b can equal 1/2 or b can be - 1/2. Both answers are bases that are possible. I suspect you are intended to write y = (1/2)^x

The reason the graph is sort of a mauve color is because both y = (1/2)^x and y = (-1/2)^x give the same graph. If they gave different results, one result would be blue and the other red.

However if the results are the same, the colors will mix. Blue + red = mauve.