The graph represents the function f(x) = 10(2)x.

Q: How would the graph change if the b value in the equation is decreased but remains greater than 1? Check all that apply.

The graph will begin at a lower point on the y-axis.
The graph will increase at a faster rate.
The graph will increase at a slower rate.
The y-values will continue to increase as x-increases.
The y-values will each be less than their corresponding x-values.

We want to see what will happen if we reduce the value of the rate of growth in an exponential relation, the correct options are:

The general exponential equation is:

f(x) = A*(b)^x

Where A is the initial value, and b is the rate of growth/decay.

Here we have the function:

f(x) = 10*(2)^x

Notice that b = 2, so this is exponential growth.

Now, what will happen if we decrease the value of b such that this still is greater than 1?

Now let's analyze each statement to see which ones are true:

a) "The graph will begin at a lower point on the y-axis."

False, this only depends on the initial value A, which was not changed.

b) "The graph will increase at a faster rate."

False, as larger is the value of b, faster increases the graph.

c) "The graph will increase at a slower rate."

True, we reduced the value of b, thus, it increases at a slower rate.

d) "The y-values will continue to increase as x-increases."

True, we still have an exponential growth, because b >1.

e) "The y-values will each be less than their corresponding x-values."

False, as we said above, it is an exponential growth.

If you want to learn more about exponential growth, you can read:

link

The graph will increase at a slower rate.

The y-values will continue to increase as x-increases.

Step-by-step explanation:

Since b > 1, it will be a growth function but the rate of growth would be lesser than before

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .