Once you substitute $t = 3$ and $B = 1920$, divide both sides by $1500$ so the left side becomes $r^3$.

Take the cube root of the number you get for $r^3$. Then compare that decimal to the growth factors appearing in the answer choices (the numbers inside the parentheses).

Make sure the equation you choose still has $1500$ as the starting number of bacteria at $t = 0$, as given in the original model.

In Desmos, type (1920/1500)^(1/3) and look at the decimal value it outputs. This is the approximate value of $r$ that makes $1500r^3 = 1920$.

Compare the decimal from step 1 to the growth factors in the answer choices (the numbers inside the parentheses: $1.07$, $1.08$, $1.09$). Choose the option whose growth factor is closest to the Desmos value and still has $1500$ as the initial value.

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

We are told that after $3$ hours, there are $1{,}920$ bacteria, so $B = 1920$ when $t = 3$.

Substitute these into the model:

Now solve this equation for $r$.

From

first isolate $r^3$:

Now take the cube root of both sides to get $r$:

Using a calculator, this value is a little more than $1.08$ and less than $1.09$, closer to $1.09$ than to $1.08$.

So the per-hour growth factor $r$ is approximately $1.09$.

The model keeps the initial value $1500$ and uses the growth factor $r$ you just found.

Using $r \approx 1.09$, the equation that best models the number of bacteria after $t$ hours is

which corresponds to choice D.