Researchers recorded that a certain bacteria population declined from 170,000 to 200 in 42 hours. At this rate of decay, how many bacteria was there at 24 hours? Round to the nearest whole number.

3600 bacterias

Step-by-step explanation:

From P = P'e^(-kt), where

P = final population

P' = initial population

k = decay constant

t = time in hrs

Substituting we have

200 = 170000 x e^(-42k)

1/850 = e^(-42k)

We take natural log (Ln) of both side

Ln (1/850) = Ln (e^(-42k))

-6.745 = -42k

k = 0.16059.

For amount remaining after 24 hrs we find P

P = 170000 x e^(-0.16059x24)

P = 170000 x e^-3.85416

P = 170000 x 0.02119 = 3602.3

Approximately 3600 bacterias.

answer: domain and range mean all possible values of x and y that could be substituted to the inequality. a solution means all possible values that make the inequality statement true. so while the range is still all real numbers, the solution is the shaded area, for which y will always be greater than the line of the function.