Question

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

On a coordinate plane, an exponential growth function approaches y = 0 in the second quadrant and goes through points (negative 1, 5), (0, 10), (1, 20), (2, 40).
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.

Answer 1

Answer:

The graph will increase at a slower rate

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

Step-by-step explanation:

we have the exponential function

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

This is a exponential growth function, because the base of the exponential function is greater than 1 (b=2)

If the b value in the equation is decreased but remains greater than 1, the exponential equation will continue to be a exponential growth function

so

Verify each statement

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

The statement is false

Because, the graph will begin at the same initial value than the original function. The initial value for both cases is 10

2) The graph will increase at a faster rate.

The statement is false

Because, the graph will increase at a slower rate

3) The graph will increase at a slower rate.

The statement is true

Because, if the b value in the equation is decreased, the rate of change is decreased too

4) The y-values will continue to increase as x-increases

The statement is true

Because the function continue to be a exponential growth function

5) The y-values will each be less than their corresponding x-values

The statement is false

Because, the y-values will each be greater than their corresponding x-values

Answer 2

Answer:

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C. The graph will increase at a slower rate.

and

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

Step-by-step explanation: