Answer:
151,031
Step-by-step explanation:
If the population of a town is decreasing at 0.8% each year, the new population of the town will be
of what it was last year. To find 99.2% of something, multiply it by 0.992. Therefore, we can write the following equation:
, where
is the population of the town
years after the town had a population of 157,220.
Substitute
into this equation to get the projected population after 5 years:
![f(5)=157,220\cdot 0.992^5, \\f(5)=151031.019048,\\f(5)\approx \boxed{151,031}](https://tex.z-dn.net/?f=f%285%29%3D157%2C220%5Ccdot%200.992%5E5%2C%20%5C%5Cf%285%29%3D151031.019048%2C%5C%5Cf%285%29%5Capprox%20%5Cboxed%7B151%2C031%7D)
Therefore, in 5 years, the population should be 151,031.
Answer:
A)3x + 4y = 8
Step-by-step explanation:
Given expression;
y =
- 7
A line perpendicular to this will have negative inverse slope;
the slope of the given line =
perpendicular line =
Now;
the equation of the line is;
y =
x - 7
multiply through by 4
4y = -3x - 28
4y + 3x = -28
Answer:
Step-by-step explanation:
1. Draw a line down the middle of the equal sign .
2.Divide 4x/4. Which equals x.
3. Divide 6/4. Which equals 1 and 2/4 or 1 and 1/2.
4. X=1 2/4
5. Check=
Y=4x+6
Plug 4 with 1 2/4. Which equals 6.
6+6=12
X=1 2/4 Y=12
Answer:
A: (-1,0)
B: (1,1)
C: (5,3)
(0,½)
(7,5) doesn't lie on the line
Step-by-step explanation:
Slope: (3-1)/(5-1) = ½
y = ½x + c
0 = ½(-1) + c
c = ½
y = ½x + ½
(0,½) is on the line
y = ½x + ½
Check for (7,5)
5 = 7/2 + 1/2
5 = 4 is a false statement
Answer:
a)Average cost function =![\bar{C(x)}=\frac{1000+0.1x}{x}](https://tex.z-dn.net/?f=%5Cbar%7BC%28x%29%7D%3D%5Cfrac%7B1000%2B0.1x%7D%7Bx%7D)
Marginal cost function =![C'x=0.1](https://tex.z-dn.net/?f=C%27x%3D0.1)
b) ![\bar{C(2000)}=0.6](https://tex.z-dn.net/?f=%5Cbar%7BC%282000%29%7D%3D0.6)
![C'(2000)=0.1](https://tex.z-dn.net/?f=C%27%282000%29%3D0.1)
c)
is the average cost to produce first 2000 items
C'(2000)=0.1 is the marginal cost to produce 2001 th item
Step-by-step explanation:
Cost function: ![C(x) = 1000 + 0.1x](https://tex.z-dn.net/?f=C%28x%29%20%3D%201000%20%2B%200.1x)
a)Find the average cost and marginal cost functions.
Average cost function =![\bar{C(x)}=\frac{C(x)}{x}](https://tex.z-dn.net/?f=%5Cbar%7BC%28x%29%7D%3D%5Cfrac%7BC%28x%29%7D%7Bx%7D)
Average cost function =![\bar{C(x)}=\frac{1000+0.1x}{x}](https://tex.z-dn.net/?f=%5Cbar%7BC%28x%29%7D%3D%5Cfrac%7B1000%2B0.1x%7D%7Bx%7D)
Marginal cost function =![C'x=0.1](https://tex.z-dn.net/?f=C%27x%3D0.1)
b) Determine the average and marginal cost when x = a.
a = 2000
Average cost function =![\bar{C(x)}=\frac{1000+0.1x}{x}=\frac{1000+0.1a}{a}=\frac{1000+0.1(2000)}{2000}=0.6](https://tex.z-dn.net/?f=%5Cbar%7BC%28x%29%7D%3D%5Cfrac%7B1000%2B0.1x%7D%7Bx%7D%3D%5Cfrac%7B1000%2B0.1a%7D%7Ba%7D%3D%5Cfrac%7B1000%2B0.1%282000%29%7D%7B2000%7D%3D0.6)
So, ![\bar{C(2000)}=0.6](https://tex.z-dn.net/?f=%5Cbar%7BC%282000%29%7D%3D0.6)
Marginal cost function =![C'(2000)=0.1](https://tex.z-dn.net/?f=C%27%282000%29%3D0.1)
c)Interpret the values obtained in part (b).
is the average cost to produce first 2000 items
C'(2000)=0.1 is the marginal cost to produce 2001 th item