Homework 7

When typing answers, give exact answers unless indicated otherwise. If a function is needed in order to give an exact answer, just list the function's normal abreviation with its input value such as: ln#, sqrt(#), etc. Only use parenthesis where needed. Do not use square or curley brackets. If you are sure that you have a correct answer, but you are getting it marked wrong, try writing it in a different format.

hmwk7 #1) A certain piece of real estate has been increasing in value by 10% every 2 years. It was worth $55,000 at the beginning of 1980.

Question 1) What was it worth at the beginning of 1996?
Question 2) Assuming the same trend, in what year was it or will it be worth $200,000?

hmwk7 #2) Let a and b be real numbers such that 0<a<1 and 1<b. Match the following equations to their graphs.

1.  y = ax 2.  y = bx 3.  y = log ax 4.  y = log bx

A.   B.

C.   D.

hmwk7 #3) Evaluate: (You should be able to do all 5 of these in less than one minute.)

1.   logbb = 2.   logb1 = 3.   logbbx = 4.   10log x = 5.   ln e =

A.   -1 B.   0 C.   1 D.   e E.   10 F.   x G.   b H.   bx I.   xb

hmwk7 #4) Let log_b r = 2, log_b s = 5, and log_b w = 7. Evaluate:

Question 1) log_b (s/(rw)) =
Question 2) log_b (sw) =
Question 3) log_b w³ =

hmwk7 #5) The following equation has no real solutions. There are two complex solutions: a + b i and a - b i which can be found algebraically without a calculator and without logarithms. Find a and b. Write your answer in the following format: a, b

hmwk7 #6) Use logarithms to solve 7^x = 21. Round your answer to the nearest thousandths place. For example, if your answer is 2.364876, you would write: 2.365

hmwk7 #7) Find c and k so that y = 2(1.10) ^x is equivalent to y = ce ^kx. Give exact answers.