The exponential function given is
\[ y = \frac{3}{4} \left( \frac{7}{2} \right)^x. \]
In an exponential function of the form
\[ y = a \cdot b^x, \]
where \(a\) is the initial value and \(b\) is the base of the exponential, the growth rate is determined by \(b\).
In this case, the base \(b\) is \(\frac{7}{2}\). To determine the growth rate, we can interpret this as
\[ b - 1. \]
Calculating the growth rate:
\[ \text{Growth rate} = \frac{7}{2} - 1 = \frac{7}{2} - \frac{2}{2} = \frac{5}{2}. \]
So, the growth rate in terms of a fractional increase is \( \frac{5}{2} \) or 2.5.
If you were looking for answers from the options you provided:
- \( \frac{4}{3} \)
- \( \frac{7}{2} \)
- \( \frac{3}{4} \)
- \( \frac{2}{7} \)
None of these represent the growth rate correctly. The growth rate is \( \frac{5}{2} \), which is equivalent to 2.5.