Answer:
The inverse for log₂(x) + 2 is - log₂x + 2.
Step-by-step explanation:
Given that
f(x) = log₂(x) + 2
Now to find the inverse of any function we put we replace x by 1/x.
f(x) = log₂(x) + 2
f(1/x) =g(x)= log₂(1/x) + 2
As we know that
log₂(a/b) = log₂a - log₂b
g(x) = log₂1 - log₂x + 2
We know that log₂1 = 0
g(x) = 0 - log₂x + 2
g(x) = - log₂x + 2
So the inverse for log₂(x) + 2 is - log₂x + 2.
The question asks per week. So 1.5 cups times 7 days is 10.5 cups.
The pipe leaks 10.5 cups every week.
Some basic dimensions could be 4x1 and 3x2
From calculus, to determine the maxima or minima of the graph, get the derivative of the equation and equate to zero. So, we derive first the equation of the graph and equate to zero.
C = 0.25x² - 80x + 30000
dC/dx = 0 = 0.5x - 80 + 0
0.5x = 80
x = 80/0.5
x = 160 units
The minimum cost (although not asked) is:
C = 0.25(160)² - 80(160) + 30000
C = $23,600
The answer is 160 units.
