Answer:
a huge part of this question is missing
Answer:
$13,304
Step-by-step explanation:
-We use the compound interest function to determine the rate of growth.
-Given that the amount doubles in 13 years, the annual growth rate is calculated as:
![A=P(1+i)^n\\\\2P=P(1+i)^n\\\\\therefore 2=(1+i)^{13}\\\\i=2^{1/13}-1=0.05477](https://tex.z-dn.net/?f=A%3DP%281%2Bi%29%5En%5C%5C%5C%5C2P%3DP%281%2Bi%29%5En%5C%5C%5C%5C%5Ctherefore%202%3D%281%2Bi%29%5E%7B13%7D%5C%5C%5C%5Ci%3D2%5E%7B1%2F13%7D-1%3D0.05477)
We now substitute this value of i in the compound interest formula equation to solve for future value:
![A=P(1+i)^n\\\\\\=7400(1.05477)^{11}\\\\\\=13303.54](https://tex.z-dn.net/?f=A%3DP%281%2Bi%29%5En%5C%5C%5C%5C%5C%5C%3D7400%281.05477%29%5E%7B11%7D%5C%5C%5C%5C%5C%5C%3D13303.54)
![\approx13304](https://tex.z-dn.net/?f=%5Capprox13304)
Hence, the future value to the nearest dollar is $13,304
*You can alternatively use the exponential growth function:
![P_t=P_oe^{rt}\\\\2=e^{13r}\\\\r=\frac{In \ 2}{13}=0.05332\\\\\therefore P_{11}=7400e^{0.05332\times 11}\\\\=13303.14](https://tex.z-dn.net/?f=P_t%3DP_oe%5E%7Brt%7D%5C%5C%5C%5C2%3De%5E%7B13r%7D%5C%5C%5C%5Cr%3D%5Cfrac%7BIn%20%5C%202%7D%7B13%7D%3D0.05332%5C%5C%5C%5C%5Ctherefore%20P_%7B11%7D%3D7400e%5E%7B0.05332%5Ctimes%2011%7D%5C%5C%5C%5C%3D13303.14)
This is slightly off by just $1
Answer:
The river is 3.15 feet deep.
Step-by-step explanation:
First let's recognize what we need to find: the depth of the river
We know last year the river was 4.2 feet deep, but it dropped 25%. This means we also need to find how much it dropped. To find this, we need to know what 25% of 4.2 is. Write an equation for this.
y = 25% of 4.2
y = 0.25 • 4.2
y = 1.05
This means that the river dropped 1.05 feet. To know its depth now, we need to subtract 1.05 from 4.2. Write an equation for this.
d = 4.2 - 1.05
d = 3.15
The river is 3.15 feet deep.
Hope this helps!
Answer:
2
Step-by-step explanation:
Let f(x) = 2x – 1
Substitute (x + b) in place of x.
f(x + b) = 2(x + b) – 1
= 2x + 2x –1
To find
:
![\frac{f(x+b)-f(x)}{(x+b)-x}=\frac{(2x+2b-1)-(2x-1)}{(x+b)-x}](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28x%2Bb%29-f%28x%29%7D%7B%28x%2Bb%29-x%7D%3D%5Cfrac%7B%282x%2B2b-1%29-%282x-1%29%7D%7B%28x%2Bb%29-x%7D)
![=\frac{2x+2b-1-2x+1}{x+b-x}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B2x%2B2b-1-2x%2B1%7D%7Bx%2Bb-x%7D)
(Cancel common term)
![=2](https://tex.z-dn.net/?f=%3D2)
Hence, ![\frac{f(x+b)-f(x)}{(x+b)-x}=2.](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28x%2Bb%29-f%28x%29%7D%7B%28x%2Bb%29-x%7D%3D2.)