Exponential Functions worksheet with 14 problems for evaluating functions at given values.

Sure! Let’s solve each of the 14 exponential function evaluation problems step by step. The instructions say to evaluate each function at the given value and round to the nearest hundredth if needed.

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1) g(n) = 3 · (7/6)^n at n = -3

We substitute n = -3:

g(-3) = 3 · (7/6)^(-3)
= 3 · (6/7)^3 ← because a^(-n) = 1/a^n = (1/a)^n
= 3 · (216 / 343)
= 648 / 343 ≈ 1.89

✔ Answer: 1.89

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2) h(x) = 9 · (1/2)^x at x = 3

h(3) = 9 · (1/2)^3
= 9 · (1/8)
= 9/8 = 1.125 → round to nearest hundredth → 1.13

✔ Answer: 1.13

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3) f(n) = (4/7) · (1/2)^n at n = -3

f(-3) = (4/7) · (1/2)^(-3)
= (4/7) · 2^3
= (4/7) · 8
= 32/7 ≈ 4.57

✔ Answer: 4.57

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4) h(n) = (1/7) · 2^n at n = 2

h(2) = (1/7) · 2^2
= (1/7) · 4
= 4/7 ≈ 0.57

✔ Answer: 0.57

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5) g(y) = (9/3) · (1/2)^y at y = 2

Note: 9/3 = 3

g(2) = 3 · (1/2)^2
= 3 · (1/4)
= 3/4 = 0.75

✔ Answer: 0.75

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6) h(x) = 5 · 2^x at x = 3

h(3) = 5 · 2^3
= 5 · 8 = 40

✔ Answer: 40

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7) f(x) = 3 · (5/7)^x at x = 3

f(3) = 3 · (5/7)^3
= 3 · (125 / 343)
= 375 / 343 ≈ 1.09

✔ Answer: 1.09

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8) h(n) = (1/2) · (1/3)^n at n = -2

h(-2) = (1/2) · (1/3)^(-2)
= (1/2) · 3^2
= (1/2) · 9 = 9/2 = 4.5

✔ Answer: 4.50

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9) g(y) = (2/7) · 2^y at y = 2

g(2) = (2/7) · 2^2
= (2/7) · 4
= 8/7 ≈ 1.14

✔ Answer: 1.14

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10) f(y) = (3/2) · 2^y at y = -2

f(-2) = (3/2) · 2^(-2)
= (3/2) · (1/4)
= 3/8 = 0.375 → round to nearest hundredth → 0.38

✔ Answer: 0.38

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11) f(x) = 4 · 2^x at x = -2

f(-2) = 4 · 2^(-2)
= 4 · (1/4) = 1

✔ Answer: 1.00

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12) h(y) = (1/2) · (1/3)^y at y = 3

h(3) = (1/2) · (1/3)^3
= (1/2) · (1/27)
= 1/54 ≈ 0.02

✔ Answer: 0.02

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13) g(y) = (1/2) · (2/3)^y at y = -2

g(-2) = (1/2) · (2/3)^(-2)
= (1/2) · (3/2)^2
= (1/2) · (9/4)
= 9/8 = 1.125 → round to nearest hundredth → 1.13

✔ Answer: 1.13

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14) g(y) = 8 · (1/2)^y at y = -2

g(-2) = 8 · (1/2)^(-2)
= 8 · 2^2
= 8 · 4 = 32

✔ Answer: 32

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## ✔ Final Answers Summary:

1) 1.89
2) 1.13
3) 4.57
4) 0.57
5) 0.75
6) 40
7) 1.09
8) 4.50
9) 1.14
10) 0.38
11) 1.00
12) 0.02
13) 1.13
14) 32

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