Givens
Petri Dish A sees a double ever 10 minutes
Petri Dish B sees a double ever 6 minutes
Consequences
A doubles 60 / 10 = 6 times.
B doubles 60 / 6 = 10 times.
Solution
If you work best with numbers then suppose there are 100 bacteria in both dishes at the beginning
A = 100 * 2^6
B = 100 * 2^10
A will have 100 * 64 = 6400 bacteria growing inside A
B will have 100 * 1024 = 102400 bacteria growing inside B
B/A = 102400 / 6400 = 16
There are 16 times as many in B than in A. <<<< Answer
Answer:
(a) The average cost function is 
(b) The marginal average cost function is 
(c) The average cost approaches to 95 if the production level is very high.
Step-by-step explanation:
(a) Suppose 
is a total cost function. Then the average cost function, denoted by 
, is
We know that the total cost for making x units of their Senior Executive model is given by the function
The average cost function is
(b) The derivative 
of the average cost function, called the marginal average cost function, measures the rate of change of the average cost function with respect to the number of units produced.
The marginal average cost function is
(c) The average cost approaches to 95 if the production level is very high.
![\lim_{x \to \infty} (\bar{C}(x))=\lim_{x \to \infty} (95+\frac{230000}{x})\\\\\lim _{x\to a}\left[f\left(x\right)\pm g\left(x\right)\right]=\lim _{x\to a}f\left(x\right)\pm \lim _{x\to a}g\left(x\right)\\\\=\lim _{x\to \infty \:}\left(95\right)+\lim _{x\to \infty \:}\left(\frac{230000}{x}\right)\\\\\lim _{x\to a}c=c\\\lim _{x\to \infty \:}\left(95\right)=95\\\\\mathrm{Apply\:Infinity\:Property:}\:\lim _{x\to \infty }\left(\frac{c}{x^a}\right)=0\\\lim_{x \to \infty} (\frac{230000}{x} )=0](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%28%5Cbar%7BC%7D%28x%29%29%3D%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%2895%2B%5Cfrac%7B230000%7D%7Bx%7D%29%5C%5C%5C%5C%5Clim%20_%7Bx%5Cto%20a%7D%5Cleft%5Bf%5Cleft%28x%5Cright%29%5Cpm%20g%5Cleft%28x%5Cright%29%5Cright%5D%3D%5Clim%20_%7Bx%5Cto%20a%7Df%5Cleft%28x%5Cright%29%5Cpm%20%5Clim%20_%7Bx%5Cto%20a%7Dg%5Cleft%28x%5Cright%29%5C%5C%5C%5C%3D%5Clim%20_%7Bx%5Cto%20%5Cinfty%20%5C%3A%7D%5Cleft%2895%5Cright%29%2B%5Clim%20_%7Bx%5Cto%20%5Cinfty%20%5C%3A%7D%5Cleft%28%5Cfrac%7B230000%7D%7Bx%7D%5Cright%29%5C%5C%5C%5C%5Clim%20_%7Bx%5Cto%20a%7Dc%3Dc%5C%5C%5Clim%20_%7Bx%5Cto%20%5Cinfty%20%5C%3A%7D%5Cleft%2895%5Cright%29%3D95%5C%5C%5C%5C%5Cmathrm%7BApply%5C%3AInfinity%5C%3AProperty%3A%7D%5C%3A%5Clim%20_%7Bx%5Cto%20%5Cinfty%20%7D%5Cleft%28%5Cfrac%7Bc%7D%7Bx%5Ea%7D%5Cright%29%3D0%5C%5C%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%28%5Cfrac%7B230000%7D%7Bx%7D%20%29%3D0)
Answer:
a=(2,8) b=(8,8)
c=(8,2) d=(2,2)
Step-by-step explanation:
Let no. of pens be x.
Pens : x
Pencils: x+8
Total: 2x+8
Student takes 1 pen and 5 pencils.
Remainder: 2x+8 - 5 -1 = 2x+2
2x+2 = 26
2x= 24
x = 12 (original no. of pens)
x+ 8 = 20 (original no of pencils)
There are 12 pens at first and 20 pencils.
After 1 pen is taken, 11 pens are left.
After 5 pencils are taken, 20-5=15 pencils are left.
Answer:
4m(4m-3)
Step-by-step explanation:
16m^2 − 12m
16 m^2 = 2*2*2*2*m*m
12m = 2*2*3*m
The greatest factor for 16m^2 and 12m is 2*2*m or 4m
Factor out 4m
16 m^2 = 2*2*2*2*m*m = 4m(2*2m)=4m(4m)
12m = 2*2*3*m = 4m(3)
Factoring out 4m
16m^2 − 12m
4m(4m-3)
