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f(t)=80(4)^(t) Which of the following is an equivalent form of the function f in which the base of the exponent is 2 ? Choose 1 answer: (A) f(t)=80(2)^((t)/(2)) (B) f(t)=80(2)^(t+2) (C) f(t)=80(2)^(2t) (D) f(t)=160(2)^(t)

f(t)=80(4)t f(t)=80(4)^{t} \newlineWhich of the following is an equivalent form of the function f f in which the base of the exponent is 22 ?\newlineChoose 11 answer:\newline(A) f(t)=80(2)t2 f(t)=80(2)^{\frac{t}{2}} \newline(B) f(t)=80(2)t+2 f(t)=80(2)^{t+2} \newline(C) f(t)=80(2)2t f(t)=80(2)^{2 t} \newline(D) f(t)=160(2)t f(t)=160(2)^{t}

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Q. f(t)=80(4)t f(t)=80(4)^{t} \newlineWhich of the following is an equivalent form of the function f f in which the base of the exponent is 22 ?\newlineChoose 11 answer:\newline(A) f(t)=80(2)t2 f(t)=80(2)^{\frac{t}{2}} \newline(B) f(t)=80(2)t+2 f(t)=80(2)^{t+2} \newline(C) f(t)=80(2)2t f(t)=80(2)^{2 t} \newline(D) f(t)=160(2)t f(t)=160(2)^{t}
  1. Understand Relationship: Understand the relationship between the bases 44 and 22. Since 44 is a power of 22, we can express 44 as 22 squared (4=224 = 2^2).
  2. Substitute Expression: Substitute the expression for 44 in terms of 22 into the function.\newlinef(t)=80(4)tf(t) = 80(4)^{t} can be rewritten as f(t)=80(22)tf(t) = 80(2^2)^{t}.
  3. Apply Power Rule: Apply the power of a power rule.\newlineAccording to the power of a power rule, (ab)c=a(b∗c)(a^b)^c = a^{(b*c)}. Therefore, f(t)=80(22)tf(t) = 80(2^2)^t becomes f(t)=80(22∗t)f(t) = 80(2^{2*t}).
  4. Compare with Answer Choices: Compare the resulting expression with the answer choices.\newlineThe expression f(t)=80(22t)f(t) = 80(2^{2t}) matches with option (C) f(t)=80(2)2tf(t)=80(2)^{2t}.

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