Writing Exponents Worksheets | Worsheets library - Free Printable

Sure! Let’s solve each of the 14 exponential function evaluation problems step by step. We’ll plug in the given value for the variable and simplify, rounding to the nearest hundredth if needed.

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1) g(n) = 3 · (7/6)^n at n = -3

We use the rule:
> a^(-n) = 1 / a^n

So:

g(-3) = 3 · (7/6)^(-3)
= 3 · (6/7)^3
= 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

First, simplify 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 = 40.00

✔ Answer: 40.00

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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 = 4.50

✔ 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 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)
= 1.00

✔ 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 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 = 32.00

✔ Answer: 32.00

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## ✔ Final Answers:

1) 1.89
2) 1.13
3) 4.57
4) 0.57
5) 0.75
6) 40.00
7) 1.09
8) 4.50
9) 1.14
10) 0.38
11) 1.00
12) 0.02
13) 1.13
14) 32.00

Let me know if you’d like to see any step explained further!