Answer:
Out of all the choices given A. seems to fit best.
The initial value is 500 so the beginning should be A(n) = 500
The rate of increase is 4% so you would put that into decimal form of 0.04
Then you plug in 0.04 into (n - 1) and since we know that it is increasing you would put (1 + 0.04)
And the question asked to find the account's balance at the beginning of year 5 so plug 5 into n in the equation
A(n) = 500(1 + 1.04)^5 = 608.33
Hope this helps!
Answer:
y=2 and 3/4
Step-by-step explanation:
Answer:
Length and Width = 10ft
Height = 5ft
Surface Area = 300 square feet
Step-by-step explanation:
Given
-- Volume
Let:
![L = Length](https://tex.z-dn.net/?f=L%20%3D%20Length)
![W =Width](https://tex.z-dn.net/?f=W%20%3DWidth)
![H = Height](https://tex.z-dn.net/?f=H%20%3D%20Height)
Volume (V) is calculated as:
Substitute 500 for V
![500 = L * W * H](https://tex.z-dn.net/?f=500%20%3D%20L%20%2A%20W%20%2A%20H)
Make H the subject
The tank has no top. So, the surface area (S) is:
![S = L * W + 2*H*L + 2*H*W](https://tex.z-dn.net/?f=S%20%3D%20L%20%2A%20%20W%20%2B%202%2AH%2AL%20%2B%202%2AH%2AW)
Substitute 500/LW for H
![S = L * W + 2*\frac{500}{LW}(L + W)](https://tex.z-dn.net/?f=S%20%3D%20L%20%2A%20%20W%20%2B%202%2A%5Cfrac%7B500%7D%7BLW%7D%28L%20%2B%20W%29)
![S = L * W + \frac{1000}{LW}(L + W)](https://tex.z-dn.net/?f=S%20%3D%20L%20%2A%20%20W%20%2B%20%5Cfrac%7B1000%7D%7BLW%7D%28L%20%2B%20W%29)
![S = L W + \frac{1000}{L} + \frac{1000}{W}](https://tex.z-dn.net/?f=S%20%3D%20L%20W%20%2B%20%5Cfrac%7B1000%7D%7BL%7D%20%2B%20%5Cfrac%7B1000%7D%7BW%7D)
Differentiate with respect to L and to W
![S'(W) = L - \frac{1000}{W^2}](https://tex.z-dn.net/?f=S%27%28W%29%20%3D%20L%20-%20%5Cfrac%7B1000%7D%7BW%5E2%7D)
and
![S'(L) = W - \frac{1000}{L^2}](https://tex.z-dn.net/?f=S%27%28L%29%20%3D%20W%20-%20%5Cfrac%7B1000%7D%7BL%5E2%7D)
Equate both to get the critical value
and ![S'(L) = W - \frac{1000}{L^2}](https://tex.z-dn.net/?f=S%27%28L%29%20%3D%20W%20-%20%5Cfrac%7B1000%7D%7BL%5E2%7D)
and ![0 = W - \frac{1000}{L^2}](https://tex.z-dn.net/?f=0%20%3D%20W%20-%20%5Cfrac%7B1000%7D%7BL%5E2%7D)
and ![\frac{1000}{L^2} = W](https://tex.z-dn.net/?f=%5Cfrac%7B1000%7D%7BL%5E2%7D%20%3D%20W)
and ![L^2W = 1000](https://tex.z-dn.net/?f=L%5E2W%20%3D%201000)
Make L the subject in ![W^2L = 1000](https://tex.z-dn.net/?f=W%5E2L%20%3D%201000)
![L = \frac{1000}{W^2}](https://tex.z-dn.net/?f=L%20%3D%20%5Cfrac%7B1000%7D%7BW%5E2%7D)
Substitute
for L in
![(\frac{1000}{W^2})^2 * W = 1000](https://tex.z-dn.net/?f=%28%5Cfrac%7B1000%7D%7BW%5E2%7D%29%5E2%20%2A%20W%20%3D%201000)
![\frac{1000000}{W^3} = 1000](https://tex.z-dn.net/?f=%5Cfrac%7B1000000%7D%7BW%5E3%7D%20%3D%201000)
Cross Multiply
![1000000 = 1000W^3](https://tex.z-dn.net/?f=1000000%20%3D%201000W%5E3)
Divide both sides by 1000
![1000 = W^3](https://tex.z-dn.net/?f=1000%20%3D%20W%5E3)
Take cube roots of both sides
![\sqrt[3]{1000} = W](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B1000%7D%20%3D%20W)
![10 = W](https://tex.z-dn.net/?f=10%20%3D%20W)
![W = 10](https://tex.z-dn.net/?f=W%20%3D%2010)
Substitute 10 for W in ![L = \frac{1000}{W^2}](https://tex.z-dn.net/?f=L%20%3D%20%5Cfrac%7B1000%7D%7BW%5E2%7D)
![L = \frac{1000}{10^2}](https://tex.z-dn.net/?f=L%20%3D%20%5Cfrac%7B1000%7D%7B10%5E2%7D)
![L = \frac{1000}{100}](https://tex.z-dn.net/?f=L%20%3D%20%5Cfrac%7B1000%7D%7B100%7D)
![L = 10](https://tex.z-dn.net/?f=L%20%3D%2010)
Recall that:![H = \frac{500}{LW}](https://tex.z-dn.net/?f=H%20%3D%20%5Cfrac%7B500%7D%7BLW%7D)
![H = \frac{500}{10*10}](https://tex.z-dn.net/?f=H%20%3D%20%5Cfrac%7B500%7D%7B10%2A10%7D)
![H = \frac{500}{100}](https://tex.z-dn.net/?f=H%20%3D%20%5Cfrac%7B500%7D%7B100%7D)
![H = 5](https://tex.z-dn.net/?f=H%20%3D%205)
So, the dimensions are:
and ![H = 5](https://tex.z-dn.net/?f=H%20%3D%205)
The surface area is:
![S = L * W + 2H(L + W)](https://tex.z-dn.net/?f=S%20%3D%20L%20%2A%20%20W%20%2B%202H%28L%20%2B%20W%29)
![S = 10*10 +2*5(10+10)](https://tex.z-dn.net/?f=S%20%3D%2010%2A10%20%2B2%2A5%2810%2B10%29)
![S = 10*10 +2*5*20](https://tex.z-dn.net/?f=S%20%3D%2010%2A10%20%2B2%2A5%2A20)
![S = 100 + 200](https://tex.z-dn.net/?f=S%20%3D%20100%20%2B%20200)
![S = 300](https://tex.z-dn.net/?f=S%20%3D%20300)
453.10/734 = .617% * 100 = 61.7% --> 62%
D. 62%