The problem requires identifying the initial value and the growth factor of an exponential function given in the form $Q(t) = ab^t$.

The function provided is: $Q(t) = \frac{25}{3^{\frac{1}{3}}}$

To rewrite this in the form $Q = ab^t$, we’ll analyze it as follows:

1. Identify the Initial Value $a$: The initial value is the value of $Q$ when $t = 0$. Substituting $t = 0$: $Q(0) = \frac{25}{3^{0}} = 25$ So, the initial value $a$ is 25.

2. Determine the Growth Factor $b$: In an exponential function of the form $Q(t) = ab^t$, $b$ represents the growth factor. From the equation, we see that $b = 3^{\frac{1}{3}}$.

   Calculating $3^{\frac{1}{3}}$ to four decimal places: $3^{\frac{1}{3}} \approx 1.4422$

So, the answers are:

• The initial value is $25$.
• The growth factor is approximately $1.4422$.

Would you like a detailed explanation of each step?

Follow-up Questions:

1. What is an exponential function, and why does it have a constant growth factor?
2. How do you interpret a growth factor that is greater than 1 versus one that is less than 1?
3. How can you convert an exponential decay function to a growth function?
4. What is the significance of the initial value in an exponential function in real-world applications?
5. How do we calculate fractional exponents, like $3^{1/3}$, without a calculator?

Tip: To better understand exponential functions, try graphing different functions and observing the effect of changes in the initial value and growth factor.