Question

Graph A represents the exponential equation y=3(5)^x and graph B represents y=5(3)^x.Which statements are true about graph A and graph B? select all•The y intercept of both are the same•The y intercept of graph B is greater than the y intercept of graph A•Both graphs rise at the same rate•Graph B rises faster than graph A•Graph A rises faster than graph B•The y intercept of graph A is greater than the y intercept of graph B

Answer 1

we are given the following functions:

`\begin{gathered} y=3(5)^x \\ y=5(3)^x \end{gathered}`

The graph of these equations is the following:

we are asked the following questions:

The y-intercept of both functions is the same. This is false since the y-intercept (the point where the graph touches the y-axis) for one of the functions is 3 and the other is 5.

The y-intercept of graph B is greater than the y-intercept of graph A. Since the y-intercept for graph A is 3 and the y-intercept for graph B is 5, this means that this statement is true.

Both graphs rise at the same rate. The rate of growth of an equation of the form:

`y=a(b)^x`

The rate of growth is the value of "b". The rate of growth for graph A is 5 and the rate of growth for graph B is 3, therefore, they are not the same.

Graph B rises faster than graph A. Since the rate of growth for graph A is 5 and the rate of growth for graph B is 3, this statement is false.

Graph A rises faster than graph B. This statement is true for the reason given above.

The y-intercept of graph A is greater than the y-intercept of graph B. This statement is false since the second statement is true.