Once you substitute $t = 3$, think about how to rearrange the equation to get $p$ by itself. What operation is currently being done to $p$?

You will have a factor of $(1.25)^3$. You can either compute this directly on a calculator or rewrite $1.25$ as the fraction $\frac{5}{4}$ to make the exponent easier to simplify.

In Desmos, type 250/(1.25^3) exactly as shown. The numerical result that Desmos displays is the value of $p$.

The model is

You are told that the colony has 250 bacteria after 3 hours, so $g(3) = 250$. Substitute $t = 3$ into the function:

This equation relates $p$ to the known amount 250.

You want to isolate $p$ in the equation

Divide both sides by $(1.25)^3$:

Now you just need to compute this value.

To make the arithmetic easier, write $1.25$ as a fraction: $1.25 = \frac{5}{4}$. Then

So

Simplify:

• First, $250 \div 125 = 2$, so $250 \cdot \frac{64}{125} = 2 \cdot 64$.
• Then, $2 \cdot 64 = 128$.

So the initial number of bacteria is 128.