Answer:
2468.11 dollars
Step-by-step explanation:
Amount that should be available after four years =3000 $
Interest rate = 5%
No of years =4
Let P be the principal invested
Then 
Hence 2468.11 dollars should be deposited to get 3000 dollars after 4 years at 5% interest.
Answer:

Step-by-step explanation:
This problem can be solved by using the expression for the Volume of a solid with the washer method
![V=\pi \int \limit_a^b[R(x)^2-r(x)^2]dx](https://tex.z-dn.net/?f=V%3D%5Cpi%20%5Cint%20%5Climit_a%5Eb%5BR%28x%29%5E2-r%28x%29%5E2%5Ddx)
where R and r are the functions f and g respectively (f for the upper bound of the region and r for the lower bound).
Before we have to compute the limits of the integral. We can do that by taking f=g, that is

there are two point of intersection (that have been calculated with a software program as Wolfram alpha, because there is no way to solve analiticaly)
x1=0.14
x2=8.21
and because the revolution is around y=-5 we have

and by replacing in the integral we have
![V=\pi \int \limit_{x1}^{x2}[(lnx+5)^2-(\frac{1}{2}x+3)^2]dx\\](https://tex.z-dn.net/?f=V%3D%5Cpi%20%5Cint%20%5Climit_%7Bx1%7D%5E%7Bx2%7D%5B%28lnx%2B5%29%5E2-%28%5Cfrac%7B1%7D%7B2%7Dx%2B3%29%5E2%5Ddx%5C%5C)
and by evaluating in the limits we have

Hope this helps
regards
Answer:
Yes!
Step-by-step explanation:
Answer:
f(x) = 9(5/3)^x
Step-by-step explanation:
f(x) = a(b^x)
x = 0
9 = a(b⁰)
9 = a
f(x) = 9(b^x)
x = 1
15 = 9(b¹l
b = 15/9
b = 5/3
f(x) = 9(5/3)^x
Answer:
the answer to your question is f(2)=0 and g(-2)=0