Answer :

semsee45

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]

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