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)

Question

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)

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Given function transformation: We are given the function f(t) = 100(1.1)^(3t) and we need to express it in a form where the exponent is just t. To do this, we need to find a base that raised to the power of t will give us the same result as (1.1)^(3t).Find equivalent base: To find the equivalent base for the exponent t, we can raise 1.1 to the power of 3 and then use that result as the new base. This is because (1.1)^(3t) is the same as (1.1^3)^t.Calculate new base: Now we calculate 1.1^3 to find the new base. 1.1^3 = 1.1 * 1.1 * 1.1 1.1^3 = 1.331Rewrite function with new base: Now we can rewrite the function f(t) using the new base we found: f(t) = 100(1.331)^t This is the equivalent form of the function with the exponent as t.Match with answer choices: Looking at the answer choices, we see that option (A) matches our calculation: (A) f(t) = 100(1.331)^t

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

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