In a lab, a colony of 100 bacteria is placed on a petri dish. The population triples every hour. 1. How would you estimate or find the population of bacteria in:

a. 4 hours?

b. 90 minutes?

c. 72 hour?

a). 8100 bacteria

b). 519 bacteria

c). Infinite

Step-by-step explanation:

Population growth of a bacteria is given by the exponential function,

f(x) =

Where f(x) = Population after time 't'

= Initial population

r = Growth rate

t = Duration after t hours

If "100 bacteria gets tripled every hour"

300 =

3 = 1 +

r = 100×(3 - 1)

r = 200

So the function is, f(x) =

a). Population after 4 hours,

    f(4) =

          = 8100 bacteria

b). Population after 90 minutes Or 1.5 hours

     f(1.5) =

             = 519.61

             ≈ 519 bacteria

c). Population after 72 hours,

    f(72) =

            = Infinite

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.