Which exponential equation is represented by the graph?

Question

(
1
point
)
Responses y
=
4
(
5
)
^
x y is equal to
4
times
5
to the x th power y
=
5
(
4
)
^
x y is equal to
5
times
4
to the x th power y
=
5
4
x y is equal to
5
raised to the
4
x power y
=
5
x
+
4
Which exponential equation is represented by the graph?

Answer 1

To determine which exponential equation is represented by the graph, we need to analyze each option carefully:

1. y = 4(5)^x

   • This represents an exponential function that starts at (0, 4) when x=0 and grows rapidly because of the base (5).

2. y = 5(4)^x

   • This function also starts at (0, 5) and grows but does so at a slower rate than the previous function since the base (4) is less than (5).

3. y = 5^(4x)

   • This is a function that grows very quickly since the exponent (4x) indicates a powerful increase as x increases.

4. y = 5^x + 4

   • This represents a function that grows exponentially (due to the 5^x term) but is shifted up by 4 units.

To confirm which option might match the graph you mentioned, you would look at key features like the y-intercept, growth rate, and shape of the curve.

Without seeing the actual graph, it’s hard to pinpoint which equation it represents. Generally, graphs of equations involving exponential terms (like those given here) can be distinguished by their starting point (y-intercept) and their growth behavior:

• If it's very rapid and starts around 4 or 5, options 1 and 2 could be candidates.
• If it seems to rise quickly due to increased exponentiation, option 3 would fit.
• If it has a horizontal asymptote near y=4 but grows due to the exponential, option 4 could be a fit.

Please refer to specific features of your graph to match it accordingly. If you provide more details about the graph's points and behavior, I can help narrow it down further.