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f(t)=100100(11.11)^{33t} Which of the following is an equivalent form of the function ff in which the exponent is tt ? Choose 11 answer: Choose 11 answer: (Choice A) f(t)=100(1.331)tf(t)=100(1.331)^t A f(t)=100(1.331)tf(t)=100(1.331)^t (Choice B) f(t)=100(3.3)tf(t)=100(3.3)^t B f(t)=100(3.3)tf(t)=100(3.3)^t (Choice C) f(t)=100(4.1)tf(t)=100(4.1)^{t} C f(t)=100(4.1)tf(t)=100(4.1)^{t} (Choice D) f(t)=300(1.1)tf(t)=300(1.1)^{t} D f(t)=300(1.1)tf(t)=300(1.1)^{t}

Full solution

Q. f(t)=100100(11.11)^{33t} Which of the following is an equivalent form of the function ff in which the exponent is tt ? Choose 11 answer: Choose 11 answer: (Choice A) f(t)=100(1.331)tf(t)=100(1.331)^t A f(t)=100(1.331)tf(t)=100(1.331)^t (Choice B) f(t)=100(3.3)tf(t)=100(3.3)^t B f(t)=100(3.3)tf(t)=100(3.3)^t (Choice C) f(t)=100(4.1)tf(t)=100(4.1)^{t} C f(t)=100(4.1)tf(t)=100(4.1)^{t} (Choice D) f(t)=300(1.1)tf(t)=300(1.1)^{t} D f(t)=300(1.1)tf(t)=300(1.1)^{t}
  1. Given function rewrite: Given function is f(t)=100(1.1)3t f(t) = 100(1.1)^{3t} .\newlineReasoning: We need to rewrite the function so that the exponent is t t .\newlineCalculation: f(t)=100((1.1)3)t f(t) = 100((1.1)^3)^t .
  2. Calculate base: Calculate (1.1)3 (1.1)^3 .\newlineReasoning: Simplify the base to find the equivalent form.\newlineCalculation: (1.1)3=1.1×1.1×1.1=1.331 (1.1)^3 = 1.1 \times 1.1 \times 1.1 = 1.331 .
  3. Substitute calculated value: Substitute 1.331 1.331 back into the function.\newlineReasoning: Replace the base with the calculated value.\newlineCalculation: f(t)=100(1.331)t f(t) = 100(1.331)^t .
  4. Compare with choices: Compare with the given choices.\newlineReasoning: Check which choice matches f(t)=100(1.331)t f(t) = 100(1.331)^t .\newlineCalculation: Choice A is f(t)=100(1.331)t f(t) = 100(1.331)^t .

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