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1. |
Find the value of a if the graph of the exponential function y = a · 3x passes through the point B(2, -3). |
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A. |
-3 |
B. |
 |
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C. |
3 |
D. |
9 |
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Hint |
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2. |
Solve log3 (x + 4) - log3 (x - 2) = 2 log3 2. |
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A. |
9 |
B. |
8 |
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C. |
4 |
D. |
6 |
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Hint |
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3. |
Find  to three decimal places. |
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A. |
2.3225 |
B. |
1.3617 |
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C. |
3.1355 |
D. |
1.6113 |
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Hint |
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4. |
Solve 3x + 4 = 7x - 1 to three decimal places. |
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A. |
2.397 |
B. |
7.483 |
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C. |
-1.993 |
D. |
1.254 |
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Hint |
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5. |
Business An analyst estimates that the computers his company just bought will depreciate at a rate of 25% per year. At this rate, approximately how long will it take a computer to depreciate to 30% of its original value? |
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A. |
5 years |
B. |
3 years |
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C. |
10 years |
D. |
4 years |
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Hint |
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6. |
Suppose that the wealth of a business owner is increasing exponentially. In 1993, he had $40 million. In 2001, he had $55 million. How much money will he have in 2010? |
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A. |
$20.3 million |
B. |
$57.2 million |
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C. |
$28.0 million |
D. |
$78.7 million |
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Hint |
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7. |
Solve log 3 x < 4. Check your solution. |
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A. |
x < 81 |
B. |
x < 64 |
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C. |
0 < x < 64 |
D. |
0 < x < 81 |
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Hint |
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8. |
Solve log 27  . |
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A. |
243 |
B. |
59049 |
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C. |
45 |
D. |
977,048 |
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Hint |
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9. |
Use log 3 4  1.26 to approximate the value of log 3 108. |
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A. |
36 |
B. |
2.38 |
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C. |
3.78 |
D. |
4.26 |
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Hint |
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10. |
Evaluate ln e3 -4x. |
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A. |
3 – 4x |
B. |
e3 – e4x |
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C. |
4x – 3 |
D. |
(3 – 4x)log 10 e |
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Hint |
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11. |
Shrinivas deposited $1300 in an account which pays 8% annual interest, compounded continuously. How long will it take to reach $3500? |
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A. |
176 years |
B. |
12.4 years |
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C. |
9.2 years |
D. |
1.2 years |
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Hint |
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12. |
Two cities have insect problems. The insects in City A increase exponentially according to the equation y = 120,000e0.04t. The insects in City B increase exponentially according to the equation y = 90,000e0.08t. In 15 years, which city will have more insects, and by approximately how much? |
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A. |
City B, by about 80,000 |
B. |
City A, by about 30,000 |
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C. |
City A, by about 80,000 |
D. |
City B, by about 30,000 |
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Hint |
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