The answer is graph number 2
Answer:
a) ![A(t) = 17500(1.0053)^{12t}](https://tex.z-dn.net/?f=A%28t%29%20%3D%2017500%281.0053%29%5E%7B12t%7D)
b) The balance after 8 years will be of $29,069.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
![A(t) = P(1 + \frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20P%281%20%2B%20%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
a)
Loan of $17,500 means that ![P = 17500](https://tex.z-dn.net/?f=P%20%3D%2017500)
6.4% interest rate means that ![r = 0.064](https://tex.z-dn.net/?f=r%20%3D%200.064)
Compounded monthly means that
. So
![A(t) = P(1 + \frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20P%281%20%2B%20%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
![A(t) = 17500(1 + \frac{0.064}{12})^{12t}](https://tex.z-dn.net/?f=A%28t%29%20%3D%2017500%281%20%2B%20%5Cfrac%7B0.064%7D%7B12%7D%29%5E%7B12t%7D)
![A(t) = 17500(1.0053)^{12t}](https://tex.z-dn.net/?f=A%28t%29%20%3D%2017500%281.0053%29%5E%7B12t%7D)
b)
This is A(8). Then
![A(8) = 17500(1.0053)^{12*8} = 29069](https://tex.z-dn.net/?f=A%288%29%20%3D%2017500%281.0053%29%5E%7B12%2A8%7D%20%3D%2029069)
The balance after 8 years will be of $29,069.
![x = - 3 + \frac{5 \sqrt{2} }{2} \\ - 3 - \frac{5 \sqrt{2} }{2}](https://tex.z-dn.net/?f=x%20%3D%20%20-%203%20%2B%20%20%5Cfrac%7B5%20%5Csqrt%7B2%7D%20%7D%7B2%7D%20%5C%5C%20%20%20-%203%20-%20%20%5Cfrac%7B5%20%5Csqrt%7B2%7D%20%7D%7B2%7D%20)
![x = .5355339 \\ - 6.5355339](https://tex.z-dn.net/?f=x%20%3D%20.5355339%20%5C%5C%20%20-%206.5355339)
I think that's what your looking for
There are 300 seats in the theater.
Step-by-step explanation:
Given,
Cost of one VIP ticket = $20
Cost of one regular ticket = $8
Worth of sold out tickets = $3600
Let,
x represent the number of VIP tickets sold
y represent the number of regular tickets sold
20x+8y=3600 Eqn 1
y = 2x Eqn 2
Putting value of y from Eqn 2 in Eqn 1
![20x+8(2x)=3600\\20x+16x=3600\\36x=3600](https://tex.z-dn.net/?f=20x%2B8%282x%29%3D3600%5C%5C20x%2B16x%3D3600%5C%5C36x%3D3600)
Dividing both sides by 36
![\frac{36x}{36}=\frac{3600}{36}\\x=100](https://tex.z-dn.net/?f=%5Cfrac%7B36x%7D%7B36%7D%3D%5Cfrac%7B3600%7D%7B36%7D%5C%5Cx%3D100)
Putting x=100 in Eqn 2
![y=2(100)\\y=200](https://tex.z-dn.net/?f=y%3D2%28100%29%5C%5Cy%3D200)
Total = x+y = 100+200 = 300
There are 300 seats in the theater.
Keywords: linear equation, substitution method
Learn more about substitution method at:
#LearnwithBrainly
The first thing we must do in this case is to define variables:
t = time to write the words
v = write speed.
w = number of words.
The correct expression is:
t = w / v
By substituting we have:
t = 1000/6
t = 166.6666667
Rounding:
t = 167 minutes
Answer:
The correct expression is:
t = w / v
The time is:
t = 167 minutes