Answer:
Option C is correct.
Step-by-step explanation:
An exponential is in the form of :
[tex]f(x) = ab^x[/tex]
where
a is the initial value and
b is the growth factor.
If b> 1 , then the graph is increasing.
if 0<b<1, then the graph is decreasing.
Given the function:
[tex]f(x) = 2^{x+3}[/tex]
we can write this as:
[tex]f(x) = 2^x \cdot 2^3 = 8 \cdot 2^x[/tex]
⇒[tex]f(x) =8 \cdot (2)^x[/tex]
Here, b = 2 > 1
y-intercept: The graph crosses the y-axis
Substitute x = 0 and solve for f(x):
[tex]f(0) =8 \cdot (2)^0[/tex]
⇒[tex]f(0) = 8[/tex]
⇒[tex]a = 8[/tex]
Graph of this function:
We make table for some values of x;
x f(x)
-1 4
0 8
1 16
2 32
Note as x increase, f(x) increases
Now, plot these points on the coordinate plane.
You can see the graph of the given function shown below.
