The problem says that $g(t)$ is measured in thousands of bacteria. If $g(3)$ is about $63$, how many actual bacteria does that correspond to?

Does $g(3)$ tell you how many bacteria were added during the first 3 hours, or does it tell you the total number of bacteria present at $t=3$? Use that to eliminate answer choices that talk about growth instead of total.

Type 50*(1.08)^3 into Desmos. Note the numerical output; this is the value of $g(3)$ in thousands of bacteria. Then multiply that value by $1,000$ to get the actual number of bacteria, and remember this is the culture’s total size 3 hours after it was introduced.

In the function $g(t)=50(1.08)^t$, the variable $t$ is the number of hours after the culture is introduced into the petri dish.

So $t=3$ means 3 hours after the culture is introduced.

The problem states that $g(t)$ models the size of the bacterial culture in thousands of bacteria.

So:

• $g(t)$ is the total number of bacteria, measured in thousands.
• That means a value of $1$ for $g(t)$ would mean $1{,}000$ bacteria, a value of $2$ would mean $2{,}000$ bacteria, and so on.

The statement $g(3)$ is approximately equal to $63$ means that the function’s output at $t=3$ is about $63$ (in its own units).

Because the units of $g(t)$ are thousands of bacteria, this corresponds to about

• $63$ thousand bacteria $=63{,}000$ bacteria.

So at $t=3$ hours, the culture’s total size is about $63{,}000$ bacteria.

Putting it all together:

• $t=3$ means 3 hours after the culture is introduced.
• $g(3) \approx 63$ means the total size of the culture at that time is about $63{,}000$ bacteria.

The only choice that correctly says “about 3 hours after the culture is introduced” and describes the culture as containing roughly 63,000 bacteria (total amount, not how much it grew) is:

A) About 3 hours after the culture is introduced, the petri dish is predicted to contain roughly 63,000 bacteria.