Math 141, Sem. I, 1998-99 (R.A. Brualdi) Handout 18 (November 16, 1998) Topic: Quiz # 5 (10 points per problem) 1. A radioactive substance Q-141 decays at a constant percentage rate of .025% every month. (a) What is its half-life (in months)? (b) A nuclear meltdown occurred on November 6, 1995 which resulted in a large area being contaminated with Q-141 at 50 parts per square meter. How many parts per square meter are there today (Nov. 6, 1998)? (c) If a safe-level is considered to be 2 parts per square meter, when (year, month, day) will the contaminated area be safe? [Use 360 days in a year, 30 days in a month.] (d) What would the constant percentage rate of decay, r, per month have to be in order that a safe level would be reached in (exactly) one year? ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Scratch work - I will not read this. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Polished solution: 2. A license plate has six symbols. The first two are letters of the alphabet (A to Z) and the last four are digits (0 to 9); e.g. SG-2949. (a) How many license plates are possible? (b) How many license plates are possible if no digit can occur more than once (but a letter may)? (e.g. DD-4713) (c) How many license plates are possible if no digit can occur more than once , AND no letter can occur more than once? (e.g. DH-4713) (d) If the first two symbols are letters and the tremaining symbols are digits, how many places for digits must there be if there are at least 1,000,000 registered cars? [Letters can be repeated and so can digits, as in part (a).] ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Scratch work - I will not read this. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Polished solution: