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Chapter 3 Test
Name___________________________________
CALCULATOR ACTIVE AFTER QUESTION #19
Decide if the function is an exponential function. If it is, state the initial value and the base.
1) y = - 4.5 · 8x
A) Not an exponential function
B) Exponential Function; base = 8; initial value = - 4.5
C) Exponential Function; base = - 36; initial value = 1
D) Exponential Function; base = x; initial value = - 4.5
1)
Solve the equation.
1
2) 2(5 - 3x) =
16
2)
Determine a formula for the exponential function.
3)
3)
Evaluate the logarithm.
1
4) log5( )
25
4)
1
5) log5
3 1
25
5)
6) ln e6
6)
Simplify the expression.
7) eln(0.2)
7)
Rewrite the expression as a sum or difference or multiple of logarithms.
8) log 8x
2
9) ln x3y2
8)
9)
Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all
variables represent positive real numbers.
10) 9 logm x - 8 logm z 2
10)
Find the exact solution to the equation.
11) log2(x - 4) = - 1
11)
12) 3 ln (x - 6) = 1
12)
2
13) 3(12 - 2x) = 729
13)
14) 3 · 5x/4 = 375
14)
Find the exact solution to the equation.
15) 4e2x - 3 = 8
15)
Solve the equation.
16) log 2 x = log 4 + log (x - 1 )
16)
17) log4(2x + 5) - log4(x - 2) = 1
17)
18) log6x + log6(x - 3) = 2 Hint: think quadratic!
18)
19) log (x + 3) = 1 - log x
19)
3
Use the change of base rule to find the logarithm to four decimal places.
92
20) log
4.5
20)
Solve the problem.
21) The number of books in a small library increases according to the function B = 6800e0.02t, where t is
measured in years. How many books will the library have after 5 years?
A) 6800
B) 15,658
C) 8561
D) 7515
22) The growth in the population of a certain rodent at a dump site fits the exponential function
A(t)= 749e0.016t, where t is the number of years since 1978. Estimate the population in the year
2000.
A) 533
B) 761
C) 1065
D) 1082
21)
22)
Find the amount accumulated after investing a principal P for t years at an interest rate r.
23) P = $530, t = 6, r = 1% compounded continuously
Formula: A = Pe^(rt)
A) $626.12
B) $873.82
C) $213,817.26
D) $562.77
23)
Determine the doubling time of the investment.
24) 4% APR compounded continuously
A) 17.33 years
B) 13.86 years
24)
Formula: A = Pe^(rt)
C) 34.66 years
D) 25.99 years
Solve the problem.
25) In the formula A = Iekt, A is the amount of radioactive material remaining from an initial amount I
at a given time t and k is a negative constant determined by the nature of the material. A certain
radioactive isotope decays at a rate of 0.3% annually. Determine the half-life of this isotope, to the
nearest year.
A) 167 yr
B) 100 yr
C) 2 yr
D) 231 yr
4
25)