20. Growth of an Account If Russ (see Exercise 19) chooses the plan with continuous compounding, how long will it take for his $60,000 to grow to $80,000?
3. (1/8) to the 2x-3= 16 to the x +1
13. e to the 4x= 4 to the x-2
15. ln (x-4) ln 3= ln(1/5) to the x power
20. Tripling Time For any amount of money invested at 6.8% annual interest compounded continuously, how long will it take to triple?
Please someone help ASAP!!!!!!!!! I don't understand any of these college algebra problems.
19
you want to solve for t
60000 e^.0675t = 80000
e^.0675t = 1.333...
ln both sides and use rules of logs
.0675t lne = ln 1.3333... ( but lne = 1)
t = ln 1.3333../.0675 = 4.26 years, appr 4 years and 3 months
3.
(1/8)^(2x-3) = 16^(x+1)
(2^-3)^(2x-3) = (2^4)^(x+1)
2^(-6x + 9 = 2^(4x + 4)
-6x + 9 = 4x + 4
-10x = -5
x = 1/2
13.
e^(4x) = 4^(x-2)
ln both sides
4x lne = (x-2)ln4
4x = ln4 x - 2ln4
4x - ln4 x = -2ln4
x(4 - ln4) = -2ln4
x = -2ln4/(4-ln4)
= appr -1.0608
15. ln(x-4) ln3 = ln(1/5)^x
no simple algebraic way to solve this, unless I misread the question. I took it the way you typed it
ran it through Wolfram and Wolfram ran out of time trying to solve it
http://www.wolframalpha.com/input/?i=solve++ln%28x-4%29*ln3+%3D+ln%281%2F5%29%5Ex
20. solve
1 e^.068t = 3
now do it the same way as #19
I'd be happy to help you with these college algebra problems. Let's go through each problem one by one:
20. Tripling Time:
To find out how long it will take for an investment to triple at 6.8% annual interest compounded continuously, we can use the continuous compound interest formula:
A = P * e^(rt)
Where:
A is the final amount (triple the initial amount),
P is the principal amount (initial investment),
e is the base of natural logarithm (approximately 2.718),
r is the annual interest rate (in decimal form), and
t is the time (in years).
In this case, we want to find the time it takes to triple the initial amount:
A = 3P (triple the principal amount)
Substituting the values into the formula:
3P = P * e^(0.068t)
Divide both sides of the equation by P to cancel it out:
3 = e^(0.068t)
To solve for t, we need to isolate the exponential term. Take the natural logarithm of both sides of the equation:
ln(3) = ln(e^(0.068t))
By the property of logarithms, ln(e^(0.068t)) can be simplified to (0.068t) * ln(e):
ln(3) = 0.068t * 1
Simplifying further:
0.068t = ln(3)
Now, divide both sides of the equation by 0.068:
t = ln(3) / 0.068
Using a calculator, ln(3) ≈ 1.0986. Substituting this value into the equation, we get:
t ≈ 1.0986 / 0.068
Calculating this division will give you the approximate time it takes to triple the initial amount at 6.8% annual interest compounded continuously.
I hope this explanation helps you understand how to approach and solve this problem. If you have any more questions, feel free to ask!