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I just need help with the answers. I did not have a group for the 2 questions that said it was a group project.
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Explanation & Answer
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1. 𝟒𝒙 (positive and increasing everywhere) (A).
2. By definition of logarithm this means 𝟓𝟐 = 𝟐𝟓.
𝑥3
3. log 8 𝑦 3 𝑧 3 = 𝟑 𝐥𝐨𝐠 𝟖 𝒙 − 𝟑 𝐥𝐨𝐠 𝟖 𝒚 − 𝟑 𝐥𝐨𝐠 𝟖 𝒛 (D).
4. The exponents must be the same, i.e.
−4𝑥 2 = 3𝑥 2 − 14𝑥, 7𝑥 2 − 14𝑥 = 7𝑥(𝑥 − 2) = 0,
so 𝑥 = 𝟎 or 𝑥 = 𝟐.
5. The last,
The graphs are similar, they differ only by vertical position. Note that 𝑦(−1) = 5 + log 1 = 5
and 𝑦(0) = 5 + log 2 ∈ (5, 6).
6. True. When 𝑥 → −∞, 𝑦(𝑥) → −5, so 𝑦 = −5 is a (horizontal) asymptote.
7. Arguments of logs must be the same, i.e. 1 − 𝑥 = 100, so 𝑥 = 1 − 100 = −𝟗𝟗 (D).
𝑥
𝒙 𝟑
8. 3(log 𝑥 − log 𝑦) = 3 log 𝑦 = 𝐥𝐨𝐠 (𝒚) (E).
9. 𝑒 0 = 1 so the factor before exponent must be 5. Because 𝑦(4) = 1 < 5, the exponent is
decreasing. So, the answer is 𝑦 = 𝟓𝒆−𝟎.𝟒𝟎𝟐𝟒𝒙 (A).
ln 8
10. Apply ln to both sides and obtain 𝑥 ln 5 = ln 8, i.e. 𝑥 = ln 5 ≈ 𝟏. 𝟐𝟗𝟐 (E).
11. The function is always decreasing and tends to minus infinity, so B
12. By definition of logarithm this means 𝐥𝐨𝐠 𝟐 𝟖 = 𝟑.
13. It is 𝑃(6) = 1200𝑒 0.052∙6 = 1200𝑒 0.312 ≈ 1200 ∙ 1.366 ≈ 1639 (round to the closest
integer because it is the number of bacteria).
14. Apply exponent to both sides and obtain 2𝑥 = 𝑒 3 , 𝑥 =
𝑒3
2
≈ 10.043.
15. False. Consider 𝑥 = 8, the equation would be ln 1 = ln 8 − ln 7. But it is incorrect
because the left part is zero while the right part is not.
6. Miniature Golf.
a. The point of reflection has the y-coordinate of 𝟖 (𝑓𝑡) as the entire upper side h...