Respuesta :

General Idea:

The exponential function will be of the form[tex] y=a(b)^x [/tex].

When b>1, the function indicates the exponential growth.

When 0<b<1, the function indicates the exponential decay.

Applying the concept:

We are given the graph of [tex] y=10(2)^x [/tex], here b = 2.

The question ask the characteristic of the function when b is in the interval [tex] 1<b< 2 [/tex]. The attached figure shows few graphs of exponential function whose b value is less than 2 and greater than 1. We can notice that graph increases at slower rate, that is change in y with respect to change in x is getting slower as we reduce the values of b less than 2 and greater than 1.

Conclusion:

"The graph will increase at a slower rate"

Ver imagen berno

Answer: Hence, Third and Fourth options are correct.

Step-by-step explanation:

Since we have given that

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

Since it is in the form of exponential function:

As we know the general form of exponential function is given by

[tex]f(x)=ab^x[/tex]

Here, a denotes the initial amount.

b denotes the rate of growth.

If b is decreased but remains greater than 1.

Then, the graph will still increases but in slower rate.

and the value of y continue to increase as x increases.

Hence, Third and Fourth options are correct.

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