Question

Suppose it takes 4 hours for a certain strain of bacteria to reproduce by dividing in half. If 70 bacteria are present to begin with, the total number present after xxdays is f(x)=70⋅64x Find the total number present after 1, 2 and 3 days.

Answer 1

The total number of bacterial cells after 1, 2, and 3 days are calculated to be 4480, 286720, and 18350080 respectively by substituting these values into the function f(x)=70⋅64x.

Step-by-step explanation:

The mathematical function provided in the question, f(x)=70⋅64x, represents the population of bacteria x days after starting from 70 bacterial cells.

The number 64 is derived from having 2^6 bacterial generations per day, given a divide every 4 hours. To find the total number of bacteria after 1, 2, and 3 days, substitute these values for x in the function.

1. After 1 day: f(1)=70⋅64*1=4480
2. After 2 days: f(2)=70⋅64*2=286720
3. After 3 days: f(3)=70⋅64*3=18350080

Therefore, the total number of bacterial cells after 1, 2, and 3 days is 4480, 286720, and 18350080 respectively.

Learn more about Exponential Growth