Apopulation of bacteria is introduced into a culture. the number of bacteria p can be modeled by p(t) = 800 1 + 9t 90 + t2 , where t is the time in hours since the bacteria was introduced. find the rate of change of the population (in bacteria per hour) after 6 hours. (round your answer to one decimal place.)

Hello mate!

you know that the equation is (or at least i think this is):

p(t) = 800 + 9t/90 + t^2

You want to know the "rate of change" after 6 hours.

We know that the rate of change is the derivative of P(t) with respect to t; this is

now we want the rate of change when t = 6, then we replace t by 6 in the derivate equation:

so the rate of change after 6 hours is 12.9

where

If the equation is wrong ( because you write P(t) = 800 1 + 9t 90 + t2, and i don really know how to iterprete it) tellme and we can do the derivate again :D

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

step-by-step explanation: