After substituting, divide both sides of the equation by $1500$ to find the value of $r^3$.

Take the cube root of the value you found for $r^3$. Then consider how that decimal rounds to the same number of decimal places used in the answer choices.

The coefficient in the model represents the number of bacteria when $t=0$. Make sure the selected equation preserves the given starting value.

In Desmos, enter $\left(\frac{1920}{1500}\right)^{1/3}$. The result is approximately $1.0858$, the value of $r$ that satisfies $1500r^3=1920$.

Round the Desmos result to the nearest hundredth, since the growth factors in the choices are written to that precision. Then select the equation that also has $1500$ as its initial value.

The model has the form $B=1500r^t$.

After $3$ hours, the culture contains $1920$ bacteria, so substitute $B=1920$ and $t=3$:

Divide both sides by $1500$:

Take the cube root:

The growth factors in the choices are given to the nearest hundredth. Since $1.0858$ rounds to $1.09$, the best model is

This is choice D.