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f(t)=100(1.1)^(3t) Which of the following is an equivalent form of the function f in which the exponent is t ? Choose 1 answer: (A) f(t)=100(1.331)^(t) (B) f(t)=100(3.3)^(t) (c) f(t)=100(4.1)^(t) (D) f(t)=300(1.1)^(t)

f(t)=100(1.1)3t f(t)=100(1.1)^{3 t} \newlineWhich of the following is an equivalent form of the function f f in which the exponent is t t ?\newlineChoose 11 answer:\newline(A) f(t)=100(1.331)t f(t)=100(1.331)^{t} \newline(B) f(t)=100(3.3)t f(t)=100(3.3)^{t} \newline(C) f(t)=100(4.1)t f(t)=100(4.1)^{t} \newline(D) f(t)=300(1.1)t f(t)=300(1.1)^{t}

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Q. f(t)=100(1.1)3t f(t)=100(1.1)^{3 t} \newlineWhich of the following is an equivalent form of the function f f in which the exponent is t t ?\newlineChoose 11 answer:\newline(A) f(t)=100(1.331)t f(t)=100(1.331)^{t} \newline(B) f(t)=100(3.3)t f(t)=100(3.3)^{t} \newline(C) f(t)=100(4.1)t f(t)=100(4.1)^{t} \newline(D) f(t)=300(1.1)t f(t)=300(1.1)^{t}
  1. Given Function Manipulation: We are given the function f(t)=100(1.1)3tf(t) = 100(1.1)^{3t} and we need to find an equivalent form where the exponent is just tt. To do this, we need to manipulate the exponent so that it is no longer multiplied by 33.
  2. Exponent Property Application: We know that (am)n=am∗n(a^{m})^{n} = a^{m*n}. Using this property, we can rewrite the exponent 3t3t as tt by finding a new base that, when raised to the power of tt, is equivalent to (1.1)3t(1.1)^{3t}.
  3. Finding New Base: To find the new base, we calculate (1.1)3(1.1)^3 since this is the value that will be raised to the power of tt to give us the equivalent form.
  4. Calculate (1.1)3(1.1)^3: Now we calculate (1.1)3=1.1×1.1×1.1(1.1)^3 = 1.1 \times 1.1 \times 1.1.
  5. Multiplication Calculation: Performing the multiplication, we get 1.1×1.1×1.1=1.3311.1 \times 1.1 \times 1.1 = 1.331.
  6. Equivalent Form Calculation: Now we can write the equivalent form of the function as f(t)=100(1.331)tf(t) = 100(1.331)^{t}.

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