Here is the complete solution for evaluating each exponential function at the given value. I’ll walk through each one step by step, and round to the nearest hundredth where needed.
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1) h(n) = ½ · (⅓)ⁿ at n = -3
Recall: a⁻ⁿ = 1/aⁿ
So (⅓)⁻³ = 3³ = 27
h(-3) = ½ · 27 = 13.5
✔ Answer: 13.50
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2) f(n) = 5 · (⁷⁄₈)ⁿ at n = 3
(⁷⁄₈)³ = 343 / 512 ≈ 0.6699
f(3) = 5 × 0.6699 ≈ 3.3495 →
3.35
✔ Answer: 3.35
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3) f(n) = ⁴⁄₇ · (½)ⁿ at n = 3
(½)³ = 1/8 = 0.125
f(3) = ⁴⁄₇ × 0.125 = (4 × 0.125) / 7 = 0.5 / 7 ≈ 0.0714 →
0.07
✔ Answer: 0.07
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4) g(n) = ²⁄₆ · (⁵⁄₇)ⁿ at n = -3
Simplify ²⁄₆ = ¹⁄₃
(⁵⁄₇)⁻³ = (⁷⁄₅)³ = 343 / 125 = 2.744
g(-3) = ¹⁄₃ × 2.744 ≈ 0.9147 →
0.91
✔ Answer: 0.91
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5) f(y) = 5 · (⁷⁄₆)ʸ at y = -2
(⁷⁄₆)⁻² = (⁶⁄₇)² = 36 / 49 ≈ 0.7347
f(-2) = 5 × 0.7347 ≈ 3.6735 →
3.67
✔ Answer: 3.67
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6) f(y) = ½ · (⅓)ʸ at y = 2
(⅓)² = 1/9 ≈ 0.1111
f(2) = ½ × 0.1111 ≈ 0.0556 →
0.06
✔ Answer: 0.06
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7) g(x) = ⁷⁄₆ · 2ˣ at x = 2
2² = 4
g(2) = ⁷⁄₆ × 4 = 28/6 = 14/3 ≈ 4.6667 →
4.67
✔ Answer: 4.67
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8) g(x) = ⁸⁄₆ · (²⁄₉)ˣ at x = 3
Simplify ⁸⁄₆ = ⁴⁄₃
(²⁄₉)³ = 8 / 729 ≈ 0.01097
g(3) = ⁴⁄₃ × 0.01097 ≈ 1.3333 × 0.01097 ≈ 0.0146 →
0.01
✔ Answer: 0.01
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9) g(n) = ⁷⁄₈ · (½)ⁿ at n = -3
(½)⁻³ = 2³ = 8
g(-3) = ⁷⁄₈ × 8 = 7
✔ Answer: 7.00
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10) h(n) = ¹⁄₅ · 2ⁿ at n = -3
2⁻³ = 1/8 = 0.125
h(-3) = ¹⁄₅ × 0.125 = 0.2 × 0.125 = 0.025 →
0.03
✔ Answer: 0.03
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11) f(x) = ½ · (⁵⁄₃)ˣ at x = 2
(⁵⁄₃)² = 25/9 ≈ 2.7778
f(2) = ½ × 2.7778 ≈ 1.3889 →
1.39
✔ Answer: 1.39
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12) f(n) = 8 · 2ⁿ at n = 4
2⁴ = 16
f(4) = 8 × 16 = 128
✔ Answer: 128.00
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13) g(y) = 5 · (½)ʸ at y = -3
(½)⁻³ = 8
g(-3) = 5 × 8 = 40
✔ Answer: 40.00
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14) g(y) = ½ · (⁵⁄₃)ʸ at y = -2
(⁵⁄₃)⁻² = (³⁄₅)² = 9/25 = 0.36
g(-2) = ½ × 0.36 = 0.18
✔ Answer: 0.18
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##
✔ Final Answers:
1)
13.50
2)
3.35
3)
0.07
4)
0.91
5)
3.67
6)
0.06
7)
4.67
8)
0.01
9)
7.00
10)
0.03
11)
1.39
12)
128.00
13)
40.00
14)
0.18
Let me know if you’d like to see any steps broken down further!
Parent Tip: Review the logic above to help your child master the concept of exponential function worksheet pdf.
