The model $n(t)=2^t$ represents the number of bacteria in a petri dish after $t$ hours, where $t=0$ represents the time when the bacteria were first put into the dish.

What is the correct value and interpretation of $n(8)$?

A$n(8)=256$, so after 8 hours there are 256 bacteria.
B$n(8)=256$, so after 256 hours there are 8 bacteria.
C$n(8)=3$, so after 8 hours there are 3 bacteria.
D$n(8)=3$, so after 3 hours there are 8 bacteria.

Question

03-11-2026
Mathematics

Answered

The model $n(t)=2^t$ represents the number of bacteria in a petri dish after $t$ hours, where $t=0$ represents the time when the bacteria were first put into the dish.

What is the correct value and interpretation of $n(8)$?

A$n(8)=256$, so after 8 hours there are 256 bacteria.
B$n(8)=256$, so after 256 hours there are 8 bacteria.
C$n(8)=3$, so after 8 hours there are 3 bacteria.
D$n(8)=3$, so after 3 hours there are 8 bacteria.

Verified Answer :

Related Questions

What economic and social factors in the United States led to differing ideas about slavery in the North and the South Explain and support your answer with detai

What is the difference in temperature ranges between Crescent city Council bluffs and Cleveland

What is the important chemical that provides energy for cells to do work like active transport

AYUDAAAAAA cusntos angulos hay en la figura

Who was the 34th president of the US

Piles of aluminum cans floating at sea would be an example of a organic pollutants b macroscopic pollution c pathogen pollutants d thermal pollution

Which of the following actions supports the philosophy of capitalism ASAP A A city council decides that all companies within the city must pay their workers a c

A music club has 35 drum players If 25 of the total number of members in the club are drum players what is the total number of members in the club 60 70 120 140

Which god is important to the Hindu epics The Ramayana and The Mahabharata Ganges Suta Vishnu Bhagavad

GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-03T02:17:13-05:00

Identify the function $n(t) = 2^t$ where $t$ is time in hours and $n(t)$ is the bacterial population.
Substitute $t = 8$ into the function to calculate $n(8) = 2^8 = 256$.
Interpret the result as the population reaching 256 after 8 hours.
Conclude that the correct interpretation corresponds to choice (A), $\boxed{\text{(A)}}$.

Explanation

Problem Analysis

The problem provides a mathematical model for the population of bacteria in a petri dish, given by the function $n(t) = 2^t$. In this expression, the variable $t$ represents the elapsed time in hours since the bacteria were initially placed in the dish, and $n(t)$ denotes the population count of bacteria at time $t$. We are asked to determine the value of $n(8)$ and explain what it represents in the context of this experiment.

Evaluating the Function

To find the value of $n(8)$, we substitute the value $t = 8$ into our function:
\[n(8) = 2^8\]
We calculate the power:
\[2^1 = 2\]
\[2^2 = 4\]
\[2^3 = 8\]
\[2^4 = 16\]
\[2^5 = 32\]
\[2^6 = 64\]
\[2^7 = 128\]
\[2^8 = 256\]
Thus, the result of the calculation is $n(8) = 256$.

Interpretation and Conclusion

Having calculated $n(8) = 256$, we interpret this result based on our definitions:

The input $t=8$ corresponds to the time elapsed in hours, so we are evaluating the population after 8 hours.
The output $n(8) = 256$ represents the number of bacteria present at that time.

Therefore, after 8 hours, there are 256 bacteria in the dish. Comparing this to the given choices, option (A) correctly identifies both the numerical value and the physical interpretation of the result.

Examples

Exponential models like $n(t) = 2^t$ are frequently used in biology to represent rapid growth, such as the multiplication of bacteria or viruses. For example, if a single bacterium divides into two every hour, its population doubles at each interval, mirroring the pattern of powers of 2. By using these models, scientists can predict the number of organisms after a certain period, which is essential for studying diseases, developing vaccines, or even managing fermentation processes in food production. Understanding how to evaluate these functions helps in making accurate projections about resource needs and safety measures.