Question

At 8:00 a.m., the number of bacteria in a jar is recorded. The table below displays the pattern of growth of the bacteria. Note that r = 0 represents the starting time of

8:00 a.m.
Time f(minutes)
Develop a function, f(t), to model the number of bacteria at time r
0
1
2
3
Number of Bacteria
8
16
32
64

Answer 1

To develop a function, f(t), that models the number of bacteria at time t, you can observe that the number of bacteria is doubling with each passing minute. This suggests an exponential growth pattern.

You can represent the growth with the following function:

f(t) = a * 2^t

Where:

f(t) is the number of bacteria at time t.

t is the time in minutes.

a is the initial number of bacteria at t = 0.

In your case, at t = 0 (8:00 a.m.), there are 8 bacteria. So, a = 8.

Now, you can write the function:

f(t) = 8 * 2^t

This function models the growth of bacteria at any given time t in minutes, starting with 8 bacteria at t = 0. It reflects the doubling pattern you observed in the table.

Explanation:

Have great day!

Answer 2

The function that models the exponential growth of bacteria is f(t)=8·2^t, where t is the time in minutes, 8 is the initial amount of bacteria, and the bacteria double in count every minute.

The student is asking for a function, f(t), to model the exponential growth of bacteria in a jar starting at 8:00 a.m. We are given that the number of bacteria doubles every minute, starting with 8 at t = 0. To model this growth, we can use the equation f(t) = a · 2^kt, where a is the initial amount of bacteria, k is equal to 1 to represent the doubling every minute, and t is the time in minutes.

From the information provided, the initial amount of bacteria a=8, and since the bacteria double every minute, we have k=1. Therefore, the function that models the number of bacteria at time t is f(t)=8·2^t.