30 points pls
no fake answers pls

bacteria are the most common example of exponential growth. the table below shows the number of e-coli bacteria that would be present after each hour for the first six hours.

hours: 1 | 2 | 3 | 4 | 5 | 6
# of bacteria : 16 | 256 | 4,096 | 65,536 | 1,048,576 | 16,777,216

a. explain why this table represents exponential growth.

b. write a rule for this table.

c. determine how many bacteria will be present once 24 hours have passed.

d. suppose you started with 100 bacteria, but they still grew by the same growth factor. how would your rule change? explain your answer.

the correct answer is

c. 4

step-by-step explanation:

the given polynomial is

the degree of the polynomial is the highest exponent which is 4.

the -4 is called the leading coefficient.

this polynomial has only one term so it is a monomial.

the correct answer is option c.

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.

answer: need a picture

step-by-step explanation: