Answer:
c=2
Step-by-step explanation:
All polynomials are continuous and differentiable on the set of real numbers.
So we just need to confirm on the given interval that f(1)=f(3).
f(1)=1-12(1)+3(1)^2
f(1)=1-12+3
f(1)=-8
f(3)=1-12(3)+3(3)^2
f(3)=1-36+27
f(3)=-8
So this means there is c in (1,3) such that f'(c)=0.
To solve that equation we must differentiate.
f(x)=1-12x+3x^2
f'(x)=0-12+6x
f'(x)=-12+6x
Remember we need yo solve f'(c)=0 for c.
So we need to solve -12+6c=0.
-12+6c=0
Add 12 on both sides:
6c=12
Divide both sides by 6:
c=2
Answer:
Every 1.71 seconds, the bacteria loses 
Step-by-step explanation:
Given

Required [Missing from the question]
Every __ seconds, the bacteria loses 
First, we model the function from t/3 to t.

Apply law of indices

Evaluate each exponent
--- This gives the number of bacteria at time t
At time 0, we have:



Let r be the time 1/2 disappears.
When 1/2 disappears, we have:



So, we have:

Substitute r for t

Substitute 

Divide both sides by 8500


Take log of both sides

Apply law of logarithm

Make r the subject



<em>Hence, it reduces by 1/2 after every 1.71 seconds</em>
Answer: 15
Step-by-step explanation: Take 12 and change the -3 to a regular 3.
(12 + 3 = 15.)
Whichever number in the question that’s bigger determines what integer it will have.