When a bactericide is added to a nutrient broth in which bacteria are growing, the bacterium population continues to grow for a while, but then stops growing and begins to decline. the size of the population at time t (hours) is b equals 8 superscript 5 baseline plus 8 superscript 4 baseline t minus 8 cubed t squared .b=85+84t−83t2. find the growth rates at t equals 0 hours commat=0 hours, t equals 4 hours commat=4 hours, and t equals 8 hours.

The growth rates at t=0, t=4 and t=8 hours are 4096, 0 and -4096 respectively.

Step-by-step explanation:

Consider the provided function.

Now we need to find the growth rates at t=0, t=4 and t=8 hours.

Differentiate the above function.

First substitute t=0 in above function.

Substitute t=4 in above function.

Substitute t=8 in above function.

Hence, the growth rates at t=0, t=4 and t=8 hours are 4096, 0 and -4096 respectively.

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

x+y = 29, 5x + 2y = 100

step-by-step explanation:

i'm guessing it was a multiple first option was the correct answer