Answer:
r= 0.08 ft
Step-by-step explanation:
C= $500 per cubic foot
S=$20 per square foot of surface area
We know that
Profit = Selling price - Manufacturing price
P = S - C
Lets take r is the radius of sphere
Surface area ,A= 4πrr²
Volume ,V= 4πr³/3
P = S - C
P = 20 x 4πr² - 500 x 4πr³/3
For maximize the profit
dP/dr = 0
P = 20 x 4πr² - 500 x 4πr³/3
dP/dr = 160 πr - 2000 πr²
160 πr - 2000 πr² = 0
160 - 2000 r = 0
r= 0.08 ft
d²P/dr² = - 4000 πr
d²P/dr² is negative at all value of r that is why at r=0.08 ft ,it is maximum.
The number of ants in a colony doubles every 8 weeks.
Constant rate of change means that when the value of x increases, the y remains constant. So there is no change in the y value. In this case, the x value is the "week" and the y value is the "amount of ants".