If anyone could help me with any of these questions, that would be awesome.
Thanks in advance.
7. Express the function y = 5^x as an equivalent function with base 3.
8. Suppose money can be invested at 3.75% compunded semi-annually. Determine how long it takes for a principal to triple in value.
9. The decibel (dB) is used to measure the loudness of a sound. The equation D = 10logI models the decibel level of a sound whose intensity is I watts per square metre (W/m^2). The decibel levels of a subway train and normal conversation are 115 dB and 60 dB, respectively. How many times as intense as normal conversation is the noise of a subway train?
10. (a) solve the equation (2^x)^2 - 4(2^x) + 3 = 0
(b) Graph the function y = 2^2x - 4(2^x) + 3
(c) How is the graph in part (b) related to your answer in part (a)?
(d) Describe the graph in part (b). Explain why it has shape.
11. Prove logab = (logcb) / (logca). Hint: let x = logab, y = logcb, and z = logca.
Hello again, Philip!
Here's #8 . . .
8. Suppose money can be invested at 3.75% compunded semi-annually.
Determine how long it takes for a principal to triple in value.
Your expected to know the Compound Interest formula: .
The interest rate is 3.75% compounded semi-annually.
. . Hence: .
Semi-annually for years means periods.
The principal is dollars which will grow to dollars.
Substitute into the formula: .
Take logs: .
Therefore, the investment will take about years to triple in value.
to solve this equation use substitution: . Then your equation changed to:
to (b)I've attached a diagram of the graph
to (c): You have calculated the zeros of the function.
to (d): As you easily can see, the graph has a horizontal asymptote y = 3 if x approaches the neative infinity. Explanation: