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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.

The graph represents the function fx 102x How would the graph change if the b value in the equation is decreased but remains greater than 1 Check all that apply class=

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frika

Consider the graph of the function [tex] y=10\cdot b^x [/tex], where [tex] 1<b<2 [/tex].

1. For [tex] 1<b<2 [/tex] you have that [tex] b^0=1 [/tex] and [tex] 10\cdot b^0=10\cdot 1=10 [/tex]. This means that point (0,10) is y-intercept of this graph (the same as for function [tex] y=10\cdot 2^x [/tex]).

2. For [tex] 1<b<2 [/tex] you have that [tex] b^x<2^x [/tex], then [tex] 10 \cdot b^x<10\cdot 2^x [/tex] 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,

[tex] y=10\cdot 1.5^2=22.5 [/tex].

As you can see x<y.

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

Answer:

Option C and D.

Step-by-step explanation:

The given function is

[tex]f(x)=10(2)^x[/tex]

The general exponential function is

[tex]g(x)=a(b)^x[/tex]

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

[tex]f(x)=10(1.5)^x[/tex]

At x=0

[tex]f(x)=10(1.5)^0=10(1)=10[/tex]

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.

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