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Mathematics 122 test 3
Monday November 20, 2000
please show all your work in order to get full credit for each problem
(1) Use a calculator to evaluate each expression to the nearest hundredth:
(a) log2361
(b) 12000e–.06t when t = 3.
(2) Convert to a logarithmic equation: e2t = 9.
(3) Convert to an exponential equation: log(x–4) = –1.3
(4) Circle each true statement below:
(a) log(xy) = logx + logy for all real numbers x and y
x 
(b) lny = lnx – lny for all positive numbers x and y.
(c) The exponential function f(x) = 2x is a one-to-one function.
3
(d) If log2x = 3 then x = log
2
(5) Solve each equation below. Find the exact answer, such as 2ln3, and the
decimal approximation to the nearest hundredth.
(a) 600e.03t = 1200
(b) 20(1.05)t = 40(0.98)t
page two
(5 continued) Solve each equation below. Find the exact answer, such as 2ln3,
and the decimal approximation to the nearest hundredth.
 x 
(c) 10log –8 = 65
10 
(d) log4(x–2) + log4(x+3) = 2log46
(6) A sum of $20,000 is deposited into a bank account offering an interest rate of
8.2% A.P.R.
(a) If the bank compounds the interest 52 times each year, how much would be
in the account after 10 years?
(b) If the bank decides to compound continuously, how much would be in the
account after 10 years?
(c) Assuming that the interest is compounded continuously, by what percentage
does the balance in the account grow each year? (round to the nearest tenth of a
percent)
page three
(7) The population of a city grows exponentially at a rate of half a percent
(A.P.R. "compounded continuously") Presuming that the current population is
400,000, when will the population reach 800,000 ?
(8) Sketch the graph of each function below, stressing any asymptotes:
(a) y = log2(x–3)
1–x2
(b) y = (1–x)(5–3x)
(9) Sketch the graph of f(x) = 2(10.03x ) for 0 ≤ x ≤ 60 on the attached semi-log
paper.