Please answer^^ I will give you brainlist! Yes 5th grade math :clown face:
1 answer:
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The solution is x=5/4.
We use the properties of logs to rewrite the equation:
![\log[(\frac{x}{2})(\frac{20}{x^2})]=\log8 \\ \\\log(\frac{20x}{2x^2})=\log8 \\ \\\log(\frac{10}{x})=\log8](https://tex.z-dn.net/?f=%5Clog%5B%28%5Cfrac%7Bx%7D%7B2%7D%29%28%5Cfrac%7B20%7D%7Bx%5E2%7D%29%5D%3D%5Clog8%0A%5C%5C%0A%5C%5C%5Clog%28%5Cfrac%7B20x%7D%7B2x%5E2%7D%29%3D%5Clog8%0A%5C%5C%0A%5C%5C%5Clog%28%5Cfrac%7B10%7D%7Bx%7D%29%3D%5Clog8)
Get all of the logs on the same side of the equation y subtracting log 8:
Use the properties of logs to rewrite:
Exponentiate:
Multiply both sides by 8x:
1*8x = (10/8x)*8x
8x=10
Divide both sides by 8:
8x/8 = 10/8
x = 10/8 = 5/4
We use the properties of logs to rewrite the equation:
Get all of the logs on the same side of the equation y subtracting log 8:
Use the properties of logs to rewrite:
Exponentiate:
Multiply both sides by 8x:
1*8x = (10/8x)*8x
8x=10
Divide both sides by 8:
8x/8 = 10/8
x = 10/8 = 5/4
Part A
P = 10000 = amount deposited
r = 0.074 (decimal form of 7.4% interest rate)
t = 3 years
--------
A = P+P*r*t
A = 10000+10000*0.074*3
A = 10000+2220
A = 12220
Answer: 12,220 dollars
========================================================
Part B
P = 10000 = amount deposited
r = 0.065 (decimal form of 6.5% interest rate)
n = 4 = number of times money is compounded per year (aka quarterly)
t = 3 years
--------
A = P*(1+r/n)^(n*t)
A = 10000*(1+0.065/4)^(4*3)
A = 10000*(1+0.01625)^(12)
A = 10000*(1.01625)^(12)
A = 10000*1.21340757895955
A = 12134.0757895955
A = 12134.08
Answer: 12,134.08 dollars
========================================================
Part C
The simple interest investment is better over the first three years since 12,220 dollars (from part A) is larger than 12,134.08 dollars (from part B).
========================================================
Part D
I recommend George go with the compound interest account. Yes the interest rate is lower, so he won't get as much money over the first three years. But after that period he can choose to leave the money to collect interest, or withdraw some of it (leaving the remaining amount to collect compound interest). From year 5 and onward, the compound interest account will earn more money.
A graph and table is shown below. For the table, cells highlighted in blue represent when f(x) is larger than g(x). I'm using x in place of t for the graph. The f(x) curve is the simple interest function and the g(x) curve is the compound interest function.
