Answer:
Graph A
Step-by-step explanation:
The general form of an exponential function is:
[tex]\boxed{\begin{array}{l}\underline{\textsf{General form of an Exponential Function}}\\\\f(x)=ab^x\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$a$ is the initial value ($y$-intercept).}\\ \phantom{ww}\bullet\;\textsf{$b$ is the base (growth/decay factor) in decimal form.}\end{array}}[/tex]
The signs and values of a and b determine whether the function exhibits growth or decay:
- If a > 0 and b > 1, the function represents exponential growth.
- If a < 0 and b > 1, the function represents exponential decay.
- If a > 0 and 0 < b < 1, the function represents exponential decay.
- If a < 0 and 0 < b < 1, the function represents exponential growth.
Given function:
[tex]h(t) = 0.6 \cdot 3.2^t[/tex]
In this case:
- [tex]a = 0.6 > 0[/tex]
- [tex]b = 3.2 > 1[/tex]
Therefore, the function represents exponential growth.
The graph of exponential growth is characterized by a curve that initially increases slowly but then rises more rapidly, becoming steeper as it moves to the right.
For exponential decay, the graph is a curve that starts at a higher value and decreases gradually at first, then more rapidly, becoming less steep as it moves to the right.
So, the shape of the graph representing the given function is:
[tex]\Large\boxed{\boxed{\textsf{Graph A}}}[/tex]
