If the population is doubling every 10 years, the rate of change is 100%, for the period of 10 years, so, whatever it happens to be at the time, it grows by 100%, namely it doubles.
![\bf \textit{Periodic Exponential Growth}\\\\ A=I(1 + r)^{\frac{t}{p}}\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &4100\\ r=rate\to 100\%\to \frac{100}{100}\to &1.00\\ t=\textit{elapsed time}\to &8\\ p=period\to &10 \end{cases} \\\\\\ A=4100(1 + 1)^{\frac{8}{10}}\implies A=4100(2)^{\frac{4}{5}}\implies A=4100\sqrt[5]{2^4}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7BPeriodic%20Exponential%20Growth%7D%5C%5C%5C%5C%0AA%3DI%281%20%2B%20r%29%5E%7B%5Cfrac%7Bt%7D%7Bp%7D%7D%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0AA%3D%5Ctextit%7Baccumulated%20amount%7D%5C%5C%0AI%3D%5Ctextit%7Binitial%20amount%7D%5Cto%20%264100%5C%5C%0Ar%3Drate%5Cto%20100%5C%25%5Cto%20%5Cfrac%7B100%7D%7B100%7D%5Cto%20%261.00%5C%5C%0At%3D%5Ctextit%7Belapsed%20time%7D%5Cto%20%268%5C%5C%0Ap%3Dperiod%5Cto%20%2610%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0AA%3D4100%281%20%2B%201%29%5E%7B%5Cfrac%7B8%7D%7B10%7D%7D%5Cimplies%20A%3D4100%282%29%5E%7B%5Cfrac%7B4%7D%7B5%7D%7D%5Cimplies%20A%3D4100%5Csqrt%5B5%5D%7B2%5E4%7D)
Answer:
0,36π inches³ or simply 1.13 inches³
Step-by-step explanation:
In this case, first, we need to calculate the volume of the sphere with the formula:
V = 4πr³/3
Replacing the data we have:
V = 4π(3)³/3
V = 36 in³
Now that we have the volume we need to calculate the resulting error. In this case, using linear approximation we have to use the derivates of V and r, so we have the following:
If V = 4πr³/3
Then the derivate of V (dV) would be:
dV = 4π*3*r²/3 dr
Where dr is the error of radius so:
dV = 4π*r² dr
Solving for dV:
dV = 4*3.14*(3)²*(0.01)
dV = 1.13 in³
So at the end, we just report the volume of the sphere as
V = 36 ± 1 in³
dV =
The relationship between profit and revenue is:
Profit = Revenue - Total Cost
Since the cost is given as a function, the equation will be substituted as
Profit = Revenue - (3,250 + 5x + 0.1x²)
Now, the revenue is a linear graph because it is the number of pairs multiplied the fixed rate. So, the slope is constant.
Revenue = 110x --> this is the function for revenue
Thus, the equation for profit would be
Profit = 110x - 3,250 - 5x - 0.1x²
P = -0.1x²+105x-3,250 --> this is the function for profit
Now, to find the minimum value of x to make profit, differentiate P with respect to x and equate to 0.
dP/dx = 0 = -0.2x + 105
x = 525
Thus, the Gymnast Clothing should manufacture at least 525 pairs in order to make profit.
Answer:
$100 if you do 1 digit per house it would be $100
Step-by-step explanation:
