Exponential Functions worksheet with evaluation problems and solutions.

Let’s go through each problem one by one. We’ll plug in the given value for the variable and calculate step by step. Remember: when you see something like (¾)^(-2), that means 1 divided by (¾)^2 — or flip the fraction and make the exponent positive.

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1. m(c) = ¼ × (¾)^c at c = -2

→ (¾)^(-2) = (4/3)^2 = 16/9
→ ¼ × 16/9 = 16/36 = 4/9 ≈ 0.44

Wait — the image says 0.69? Let me double-check.

Actually, let’s recalculate carefully:

(¾)^(-2) = 1 / (¾)^2 = 1 / (9/16) = 16/9
Then ¼ × 16/9 = 16/(4×9) = 4/9 ≈ 0.444... → rounds to 0.44

But the image shows 0.69 — that might be a mistake? Or maybe I misread the function?

Wait — looking again: is it possible the function is written as “m(c) = ¼ × (¾)^c” but maybe it’s actually “m(c) = ¼ × (4/3)^c”? No, the image clearly says (¾).

Hold on — perhaps the original problem has a typo? But since we’re solving based on what’s written, let’s stick with correct math.

Actually — wait! Maybe I made an error in order of operations?

No — ¼ × (¾)^(-2) = 0.25 × (1.333...)² = 0.25 × 1.777... = 0.444...

So correct answer should be 0.44, not 0.69.

But since this is a worksheet with answers already filled in, and the user wants us to solve accurately — we must do our own calculation.

Let me check all problems independently.

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Actually — let’s restart and do ALL problems correctly from scratch, ignoring the orange answers in the image (since they may contain errors).

We are told: Evaluate each function at the given value. Round to nearest hundredth if needed.

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Problem 1: m(c) = ¼ × (¾)^c at c = -2

(¾)^(-2) = (4/3)^2 = 16/9 ≈ 1.7778
¼ × 1.7778 = 0.4444 → 0.44

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Problem 2: u(v) = ½ × (¾)^v at v = 2

(¾)^2 = 9/16 = 0.5625
½ × 0.5625 = 0.28125 → 0.28

(Image says 0.02 — way off)

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Problem 3: w(n) = ¾ × (⅔)^n at n = 2

(⅔)^2 = 4/9 ≈ 0.4444
¾ × 0.4444 = 0.3333 → 0.33

(This matches image)

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Problem 4: t(s) = ⅗ × (⅘)^s at s = -3

(⅘)^(-3) = (5/4)^3 = 125/64 ≈ 1.953125
⅗ = 0.6
0.6 × 1.953125 = 1.171875 → 1.17

(Image says 9.37 — wrong)

Wait — did I misread? Is it (⅘) or (4/5)? Same thing.

But 0.6 * (5/4)^3 = 0.6 * 125/64 = (3/5)*(125/64) = (3*125)/(5*64) = (375)/(320) = 75/64 ≈ 1.171875 → yes, 1.17

Image says 9.37 — probably swapped numerator/denominator?

If it were (5/4)^(-3) = (4/5)^3 = 64/125 = 0.512, then 0.6 * 0.512 = 0.307 — still not 9.37.

Maybe it's (4/5)^s with s=-3 → same as above.

I think image has errors. We proceed with correct math.

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Problem 5: p(f) = 5 × (¼)^f at f = 3

(¼)^3 = 1/64 = 0.015625
5 × 0.015625 = 0.078125 → 0.08

(Image says 0.02 — too low)

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Problem 6: y(h) = 2 × (½)^h at h = 4

(½)^4 = 1/16 = 0.0625
2 × 0.0625 = 0.125 → 0.13

(Image says 0.82 — way off)

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Problem 7: d(m) = ⅛ × ()^m at m = 2

(⅜)^2 = 9/64 ≈ 0.140625
⅛ = 0.125
0.125 × 0.140625 = 0.017578125 → 0.02

(Image says 0.34 — no)

Wait — ⅛ × (⅜)^2 = (1/8) × (9/64) = 9/512 ≈ 0.0176 → rounds to 0.02

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Problem 8: c(u) = 6 × (¼)^u at u = -2

(¼)^(-2) = 4^2 = 16
6 × 16 = 96 → 96.00

(Image says 216 — wrong)

Unless it’s (4/1)^u? Still 16.

Wait — if it were (1/4)^u with u=-2 → (4)^2=16 → 6*16=96.

Image says 216 — maybe it was supposed to be (1/3)^u? (1/3)^(-2)=9, 6*9=54 — no.

Or (1/2)^u? (1/2)^(-2)=4, 6*4=24 — no.

Perhaps it’s 6 × (3/2)^u? At u=-2: (3/2)^(-2)=(2/3)^2=4/9, 6*(4/9)=24/9≈2.67 — no.

I think image is incorrect here. Correct is 96.00

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Problem 9: n(r) = ⅖ × ()^r at r = -2

(⅗)^(-2) = (5/3)^2 = 25/9 ≈ 2.7778
⅖ = 0.4
0.4 × 2.7778 = 1.1111 → 1.11

(Image says 2.84 — no)

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Problem 10: b(x) = ⅙ × (⅚)^x at x = -2

(⅚)^(-2) = (6/5)^2 = 36/25 = 1.44
⅙ ≈ 0.1667
0.1667 × 1.44 ≈ 0.24 → 0.24

(Image says 0.82 — no)

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Problem 11: a(g) = ⅓ × (⅔)^g at g = -2

(⅔)^(-2) = (3/2)^2 = 9/4 = 2.25
⅓ × 2.25 = 0.75 → 0.75

(Image says 0.48 — no)

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Problem 12: e(t) = ½ × (⅕)^t at t = -3

(⅕)^(-3) = 5^3 = 125
½ × 125 = 62.5 → 62.50

(Image says 0.43 — completely wrong)

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Problem 13: f(y) = ⅕ × 8^y at y = -2

8^(-2) = 1/64 = 0.015625
⅕ = 0.2
0.2 × 0.015625 = 0.003125 → 0.00

(Rounded to hundredth — 0.00)

(Image says 0.01 — close but not exact; 0.003125 rounds to 0.00)

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Problem 14: h(d) = 9 × (¼)^d at d = -3

(¼)^(-3) = 4^3 = 64
9 × 64 = 576 → 576.00

(Image says 4608 — way off)

Unless it’s (1/4)^d with d=-3 → 64, 9*64=576.

If it were (1/2)^d? (1/2)^(-3)=8, 9*8=72 — no.

Or (1/3)^d? (1/3)^(-3)=27, 9*27=243 — no.

Image likely has typo.

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Problem 15: m(c) = ½ × (¾)^c at c = -2

Same as first problem but with ½ instead of ¼.

(¾)^(-2) = 16/9 ≈ 1.7778
½ × 1.7778 = 0.8889 → 0.89

(Image says 0.22 — no)

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Problem 16: u(v) = ⅓ × (¾)^v at v = -3

(¾)^(-3) = (4/3)^3 = 64/27 ≈ 2.37037
⅓ × 2.37037 ≈ 0.7901 → 0.79

(Image says 0.48 — no)

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After recalculating all, it appears the orange answers in the image are mostly incorrect. Since the instruction is to "solve the problem accurately", we will provide the correct calculated values.

But note: the user didn’t ask to correct the image — they just said “solve the problem”. The problem is to evaluate each function at the given value.

Since there are 16 separate evaluations, and the response format requires a single “Final Answer”, we need to interpret what is expected.

Looking back at the user’s request: “Solve the problem accurately.” and the image contains multiple problems.

In such cases, typically we list all answers.

But the Final Answer section expects one box.

Perhaps the user intends for us to verify or reproduce the answers? But the instruction says “solve accurately”.

Given the complexity, and since the image has pre-filled answers (which are often wrong), I think the best approach is to provide the correct evaluation for each, listed clearly.

However, the response format says: “Final Answer: [Provide only the final correct answer]”

This suggests perhaps one answer — but there are 16.

Re-reading the initial prompt: “The user uploaded an image containing a task.” — the task is to evaluate each function.

In educational contexts, sometimes “the problem” refers to the entire set.

To comply with format, I will list all 16 correct answers in order, as a sequence.

But let’s confirm with the first few:

Correct Answers (rounded to nearest hundredth):

1. m(-2) = 0.44
2. u(2) = 0.28
3. w(2) = 0.33
4. t(-3) = 1.17
5. p(3) = 0.08
6. y(4) = 0.13
7. d(2) = 0.02
8. c(-2) = 96.00
9. n(-2) = 1.11
10. b(-2) = 0.24
11. a(-2) = 0.75
12. e(-3) = 62.50
13. f(-2) = 0.00
14. h(-3) = 576.00
15. m(-2) = 0.89 [note: different m(c) than #1]
16. u(-3) = 0.79

But wait — problem 15 is also m(c), same name as #1, but different coefficient. That’s fine.

Now, to present in Final Answer, perhaps as a list.

Since the format doesn't specify, I'll write them in order separated by commas.

But let's double-check a couple more for accuracy.

Problem 8: c(u) = 6 × (¼)^u at u=-2 → (1/4)^(-2) = 16, 6*16=96 → correct.

Problem 12: e(t) = ½ × (⅕)^t at t=-3 → (1/5)^(-3)=125, 0.5*125=62.5 → correct.

Problem 13: f(y) = ⅕ × 8^y at y=-2 → 8^(-2)=1/64=0.015625, 0.2*0.015625=0.003125 → rounds to 0.00.

Some might argue to round 0.003125 to 0.00, yes.

Problem 14: h(d) = 9 × (¼)^d at d=-3 → (1/4)^(-3)=64, 9*64=576.

All seem correct.

So the final answer is the list of 16 values.

But to fit the format, I'll write them as:

Final Answer:
0.44, 0.28, 0.33, 1.17, 0.08, 0.13, 0.02, 96.00, 1.11, 0.24, 0.75, 62.50, 0.00, 576.00, 0.89, 0.79

Note: These are the accurate calculations. The orange answers in the image appear to have many errors.