1.The function g has defining equation g(x) = x^2 - 3x + 2. Find (and simplify) g(5+h).
2.If f(x) = 1/(2x) and g(x) = 3+x find (and simplify) the defining equation of the composition function f \circle g.
3.Find the inverse function of the function f(x) = 5x - 3.
4.The population size of a certain bacteria triples every decade. If there are 100,000 bacteria in the population to start with find the defining equation of the function which describes how many bacteria there will be after x decades.
5.You put $10,000 in a bank account which pays 8% interest per year. Find the defining equation of the function f which describes how much money you will have in the bank after x years.
6.If f is an exponential function, and f(0) = 500, and f(1) = 250, find the defining equation for f.
7.Write the logarithm equation ln(3) = 1.099 as an equation about exponents.
8.f Earthquake 1 measures 6.2 on the Richter scale, and Earthquake 2 measures 8.2 on the Richter scale, how many times bigger was Earthquake 2 than Earthquake 1? (Rephrased: By what factor was Earthquake 2 bigger than Earthquake 1?)
9.A club has 10 members. How many ways can the club choose a President, Vice President, and Treasurer? (Club rules forbid one person from holding more than one office.)
10.A club of 10 students will form a Subcommittee consisting of three students. How many different such Subcommittees can be formed?
11.A club consists of 8 seniors, 7 juniors, and 4 sophomores. A subcommittee consisting of 3 seniors, 2 juniors, and 1 sophomore will be chosen. How many different such subcommittees are there?
12.We toss two dice. What is the probability that the sum of the faces equals 9? (Give your answer as a fraction, not as a decimal.)
13.We perform the experiment "toss three coins" 1,000 times. How many times do you expect that the event "exactly one head" will occur?
14.We define the sequence a recursively by setting a_1 = 15 and a_(i+1) = a_i + 4 for all i>= 1. This sequence is arithmetic. Give the explicit description of the sequence.
15.If the sequence a is arithmetic, and a_3 = 5, and a_5 = 15, find a_9.
16.Find s_8 , the eighth term in the series corresponding to the arithmetic sequence which has a = 5 and d = 2.
17.Find the sum of the first 50 positive integers.
18.Find s_3 , the third term in the series which corresponds to the geometric sequence which has a = 8 and r = 1/4.
19.Find the infinite sum of the series which corresponds to the geometric sequences having a = 8 and r = 1/4.
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