Can someone please double check my answers.
1. What pattern does the logarithmic function exhibit?
a. y = b+a(lnx)
b. y = a+b(lnx)
c. y = ax+b
d. y = axb
I think A and B both look right..I just went with B.
2. Let f(x) = log6x and g(x) = log1/2x. For all x>1, f(x)>g(x)
TRUE?
3. What is the value of the following logarithmic expression: y=log81
1.91?
4. A total of $20,000 is invested at an annual interest rate of 6%. No matter how many years this money is invested, what is the best investment plan to earn the most money in the end?
a. Compounded quarterly
b. Compounded monthly
c. Compounded daily
d. Compounded continuously
I am really unsure about this one. I would guess D
1. To determine the pattern exhibited by the logarithmic function, you can analyze the given equation options. The general form of a logarithmic function is y = a + b(lnx), where "a" and "b" are constants.
Option a: y = b + a(lnx)
Option b: y = a + b(lnx)
Option c: y = ax + b
Option d: y = axb
Comparing the given options to the general form, options a and b are in the correct form.
To choose the correct answer, you need to determine if the constant "a" comes before or after the logarithm function (lnx). By convention, the constant "a" is typically placed before the logarithm function. Therefore, the correct answer is option b: y = a + b(lnx).
2. To compare the functions f(x) = log6x and g(x) = log1/2x, you need to analyze their behavior for x > 1.
For f(x) = log6x, the logarithm base is 6, meaning the function is increasing as x increases.
For g(x) = log1/2x, the logarithm base is 1/2, meaning the function is decreasing as x increases.
Thus, for x > 1, f(x) > g(x). Therefore, the statement is TRUE.
3. The expression y = log81 is asking for the logarithm with base 10 that gives 81 as the result. To solve this, you need to determine the exponent to which the base must be raised to obtain 81.
Using logarithmic properties, you can rewrite the equation as 10^y = 81. Taking the logarithm with base 10 of both sides, log(10^y) = log(81).
Since log(10^y) is equal to y, the equation simplifies to y = log(81). To evaluate the logarithm of 81, you need to determine what exponent the base 10 must be raised to in order to obtain 81.
The answer is y = 1.91.
4. To determine the best investment plan to earn the most money, you need to consider the compounding frequency and interest rate.
For compounding, the more frequent the compounding, the higher the final value will be.
Options a, b, and c suggest quarterly, monthly, and daily compounding, respectively. Generally, the higher the compounding frequency, the better.
However, option d suggests continuous compounding, which means the interest is continuously added to the principal without any specific compounding period. This results in the highest possible value in the end.
Therefore, the correct answer is option d: Compounded continuously.