Aculture of bacteria doubles every 2 hours.
a. explain how this situation can be modeled with a sequence.
b. if there are 500 bacteria at the beginning, how many bacteria will there be after 24 hours?

2,048,000.

Step-by-step explanation:

a. Let the initial number of bacteria = x

Since bacteria doubles every 2 hours, so the sequence will be in the form of

x, 2x, 4x, 8x, .........

This sequence is a geometric sequence with a common ratio of 2.

b. Since explicit formula for a geometric sequence is

Where, = population of bacteria after n hours.

            = Initial population

            r = common ratio

            n = number of times population got doubled

By putting the values of each term in the formula :

      =

      = 2,048,000

After 24 hours population of bacteria would be 2,048,000.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is