Bacteria are the most common example of exponential growth R

Bacteria are the most common example of exponential growth. Research and find a bacterium that grows each hour exponentially and determine how much it grows per hour.

A): Suppose you start with one single bacterium. Make a table of values showing the number of bacteria that may present after each hour for the first six hours. Then determine how many bacteria will be present once 24 hours have passed.

B): Explain why this table represents exponential growth.

C): Using this example, expain why any number raised to a power of zero is equal to one.

D): Write a rule for this table.

E): Suppose you start with 100 bacteria, but they still grew by the same growth factor. How would your rule change? Explain your answer.

Solution

E.coli doubles every twenty minutes. Starting with single bacteria the growth table would be

Estimated number of bacteria after 24 hours = 2²⁴ = 16,777,216 bacteria

B. The table represents exponential growth because with each division the number of bacteria doubles. Or in other words, the number of bacteria is increasing exponentially with base e=2 and x is the number of divisions.

C. When there is no division (i.e., x=0) the bacteria number remains 1

2⁰ = 1 bacteria

D. The rule for this table is that the number of bacteria at a particular generation can be determined by raising the power of base 2 with the number of generation.

E. Suppose we start with 100 bacteria, they still grew by same growth factor. Since the initial number is different we have to multiply 2ⁿ with 100.

The formulae becomes mx2ⁿ

Where m is the starting number of bacteria and n is the number of divisions

The table would be.