Answer:
The value of the account in the year 2009 will be $682.
Step-by-step explanation:
The acount's balance, in t years after 1999, can be modeled by the following equation.
![A(t) = Pe^{rt}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20Pe%5E%7Brt%7D)
In which A(t) is the amount after t years, P is the initial money deposited, and r is the rate of interest.
$330 in an account in the year 1999
This means that ![P = 330](https://tex.z-dn.net/?f=P%20%3D%20330)
$590 in the year 2007
2007 is 8 years after 1999, so P(8) = 590.
We use this to find r.
![A(t) = Pe^{rt}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20Pe%5E%7Brt%7D)
![590 = 330e^{8r}](https://tex.z-dn.net/?f=590%20%3D%20330e%5E%7B8r%7D)
![e^{8r} = \frac{590}{330}](https://tex.z-dn.net/?f=e%5E%7B8r%7D%20%3D%20%5Cfrac%7B590%7D%7B330%7D)
![e^{8r} = 1.79](https://tex.z-dn.net/?f=e%5E%7B8r%7D%20%3D%201.79)
Applying ln to both sides:
![\ln{e^{8r}} = \ln{1.79}](https://tex.z-dn.net/?f=%5Cln%7Be%5E%7B8r%7D%7D%20%3D%20%5Cln%7B1.79%7D)
![8r = \ln{1.79}](https://tex.z-dn.net/?f=8r%20%3D%20%5Cln%7B1.79%7D)
![r = \frac{\ln{1.79}}{8}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B%5Cln%7B1.79%7D%7D%7B8%7D)
![r = 0.0726](https://tex.z-dn.net/?f=r%20%3D%200.0726)
Determine the value of the account, to the nearest dollar, in the year 2009.
2009 is 10 years after 1999, so this is A(10).
![A(t) = 330e^{0.0726t}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20330e%5E%7B0.0726t%7D)
![A(10) = 330e^{0.0726*10} = 682](https://tex.z-dn.net/?f=A%2810%29%20%3D%20330e%5E%7B0.0726%2A10%7D%20%3D%20682)
The value of the account in the year 2009 will be $682.
Answer:
x - 5
Step-by-step explanation:
x^2 - 3x - 10
= (x + 2)(x - 5)
Sine the width is (x + 2), the length is (x - 5).
Hope this helped!
Answer:
18 Kilometers
Step-by-step explanation:
If you divide 12 by 4 you get 3, so she is going about 3 kilometers an hour. Add 3 for each hour, and you get 18 kilometers in 6 hours.
Answer:
A) B is greater
B) when C = 21, A = 5 and B = 15
C) A must be 0, 5, or 12 for C to be greater than B
Step-by-step explanation:
A) when a = -3, c = -20 and b = 4(-3)-5 so B = -17
B) when c = 21, a = 5 and b = 4(5)-5 so B = 15
C) C is greater than B when a = 0, 5, and 12
when a = 0, b = 4(0)-5 or -5
when a = 5, b = 4(5)-5 or 15
when a = 12, b = 4(12)-5 or 43
Answer:
Each circle (A, B, and C) contain shapes that all share at least one characteristic. Some shapes are contained in more than one circle because they share more than one characteristic. For example, shape 3 fits the rule for circles A and B, but not circle C. It lies within circles A and B, but not circle C.
Step-by-step explanation: