The graph represents the function f(x) = 10(2)^x. how would the graph change if the b value in the equation is decreased but remains greater than 1? check all that apply.

Consider the graph of the function , where .

1. For you have that and . This means that point (0,10) is y-intercept of this graph (the same as for function ).

2. For you have that , then and function is increasing. This means that the graph will increase at a slower rate and y-values will continue to increase as x-increases.

3. Not all y-values will be less than their corresponding x-values. For example, when b=1.5 and x=2,

.

As you can see x<y.

correct options are C and D, incorrect - A, B and E.

Option C and D.

Step-by-step explanation:

The given function is

The general exponential function is

where, a is initial value and b is growth factor.

If b>1, then g(x) is an increasing function.

If 0<b<1, then g(x) is an decreasing function.

On comparing both equation we get a=10 and b=2.

The b value in the equation is decreased but remains greater than 1.

1 < b < 2

Let b=1.5, So, the given function will

At x=0

It means the y-intercept of new function is 10.

Since b>1, therefore the y-values will continue to increase as x-increases.

1.5 < 2, it means the graph will increase at slower rate.

Thus, the correct options are C and D.

its 0.1 miles per minute

the ratio of balloons to tables is 5: 2 and the constant variation is 5.

the equation is y=5x