Answer: 11 year
P(1) = 37,100
P(4) = 58,400
The linear equation (for x ≥ 1)
P(x) = 37,100 + a(x-1)
For x = 4
58,400 = 37,100 + a(4-1)
58,400 - 37,100 = 3a
21300 = 3a
a = 7100
So, the linear equation:
P(x) = 37100 + 7100*(x-1)
P(x) = 37100 + 7100x - 7,100
P(x) = 7100x + 30000
To find when the profit should reach 108100, we can substitute P(x) by 108100.
108100 = 7100x + 30000
108100 - 30000 = 7100x
78100 = 7100x
x = 78100/7100
x = 11
Answer: 11 year
f(x) = g(x) at x = 2.
In order to find this, you look for where the two graphs intersect. In this case, they intersect at the point (2, 5). At this point, both f(x) and g(x) both equal 5. So to identify the point, we need to look at the x value of the ordered pair, which is x = 2.
Answer:
(m³/3 + 5m/2 + 3)pi
Step-by-step explanation:
pi integral [(f(x))² - (g(x))²]
Limits 0 to 1
pi × integral [(2+mx)² - (1-mx)²]
pi × integral[4 + 4mx + m²x² - 1 + 2mx - m²x²]
pi × integral [m²x² + 5mx + 3]
pi × [m²x³/3 + 5mx²/2 + 3x]
Upper limit - lower limit
pi × [m²/3 + 5m/2 + 3]
Verification:
m = 0
[pi × 2² × 1] - [pi × 1² × 1] = 3pi
[m³/3 + 5m/2 + 3]pi
m = 0
3pi
