What is $N(0)$ according to the problem? Plug $t = 0$ into $N(t) = a\cdot b^t$ and see what that tells you about $a$. Then, look at which answer choices use that same initial value.

The culture goes from 2,400 cells to 9,600 cells in 8 hours. That means it becomes 4 times as large in 8 hours. What value of $b$ makes $2400\cdot b^8 = 9600$? Which answer choice has that base?

In Desmos, type each option as a separate function, for example:

• $f(t) = 9600(1.19)^t$
• $g(t) = 2400(0.19)^t$
• $h(t) = 9600(0.19)^t$
• $k(t) = 2400(1.19)^t$

Evaluate each function at $t = 0$ by typing $f(0)$, $g(0)$, $h(0)$, and $k(0)$. Keep only the functions that give an output of 2,400, since the culture starts with 2,400 cells.

For the remaining candidate(s), evaluate at $t = 8$ (e.g., type $g(8)$ or $k(8)$). The function that outputs 9,600 at $t = 8$ is the one that correctly models the culture’s growth.

For exponential growth, the number of cells can be modeled as

where:

• $a$ is the initial amount (the value when $t=0$), and
• $b$ is the growth factor (how many times larger the culture becomes each hour).

We are told that at time $t = 0$ hours, the culture contains 2,400 cells.

Plugging $t=0$ into the general model:

So $a = N(0) = 2,400$, and the model must look like

Among the answer choices, this means the correct equation must have 2,400 as the coefficient (initial value).

Eight hours later, at $t = 8$, the culture has 9,600 cells. Substitute $t = 8$ and $N(8) = 9,600$ into the model:

Divide both sides by 2400:

Now solve for $b$ by taking the eighth root of 4:

So the model is

which matches the choice $N(t) = 2,400(1.19)^t$.