Answer:
Step-by-step explanation:
Volume =
find partial derivatives using product rule
i.e.
Using maximum for partial derivatives, we equate first partial derivative to 0.
y=0 or x+y =6
x=0 or x+4y =12
Simplify to get y =2, x = 4
thus critical points are (4,2) (6,0) (0,3)
Of these D the II derivative test gives
D<0 only for (4,2)
Hence maximum volume is when x=4, y=2, z= 4/3
Max volume is = 4(2)(4/3) = 32/3
Answer:
$800,500 (nearest dollar)
Step-by-step explanation:
The given scenario can be modeled as an <u>exponential equation</u>.
<u>General form of an exponential function</u>:
where:
If b > 1 then it is an increasing function
If 0 < b < 1 then it is a decreasing function
The initial value (a) is the value of the investment.
Therefore, a = 1,000,000.
If the investment <u>decreases</u> by 2.2% each year, then it will be 97.8% of the previous year.
Therefore, b = 97.8% = 0.978.
Substitute these values into the formula to create a general equation for the scenario:
(where x is the time, in years).
To find the value of the investment after 10 years, substitute x = 10 into the formula:
Therefore, the value of the investment after 10 years is $800,500 (nearest dollar).
Learn more about exponential functions here: