f(t)=20((1)/(8))^(t) Which of the following is an equivalent form of the function f in which the base of the exponent is (1)/(2) ? Choose 1 answer: (A) f(t)=5((1)/(2))^(t) (B) f(t)=20((1)/(2))^((t)/(4)) (C) f(t)=20((1)/(2))^(3t) (D) f(t)=20((1)/(2))^(4t)

Understand the problem: Understand the problem. We need to express the function f(t) = 20((1)/(8))^t with a base of (1)/(2) instead of (1)/(8).Express as power of: Express (1)/(8) as a power of (1)/(2). Since (1)/(8) is equal to (1)/(2)^3, we can rewrite the function using this relationship.Substitute in the function: Substitute (1)/(8) with (1)/(2)^3 in the function. f(t) = 20((1)/(2)^3)^tApply power rule: Apply the power of a power rule. When you raise a power to a power, you multiply the exponents. So, ((1)/(2)^3)^t becomes (1)/(2)^(3t). f(t) = 20((1)/(2)^(3t))Compare with answer choices: Compare the resulting function with the answer choices. The function we have now, f(t) = 20((1)/(2)^(3t)), matches one of the given answer choices.

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f(t)=20((1)/(8))^(t)
Which of the following is an equivalent form of the function
f in which the base of the exponent is
(1)/(2) ?
Choose 1 answer:
(A)
f(t)=5((1)/(2))^(t)
(B)

f(t)=20((1)/(2))^((t)/(4))
(C)
f(t)=20((1)/(2))^(3t)
(D)
f(t)=20((1)/(2))^(4t)

$f(t)=20\left(\frac{1}{8}\right)^{t}$ $\newline$ Which of the following is an equivalent form of the function $f$ in which the base of the exponent is $\frac{1}{2}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $f(t)=5\left(\frac{1}{2}\right)^{t}$ $\newline$ (B) $f(t)=20\left(\frac{1}{2}\right)^{\frac{t}{4}}$ $\newline$ (C) $f(t)=20\left(\frac{1}{2}\right)^{3 t}$ $\newline$ (D) $f(t)=20\left(\frac{1}{2}\right)^{4 t}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

f(t)=20\left(\frac{1}{8}\right)^{t}

\newline

Which of the following is an equivalent form of the function

f

in which the base of the exponent is

\frac{1}{2}

\newline

Choose

1

answer:

\newline

(A)

f(t)=5\left(\frac{1}{2}\right)^{t}

\newline

(B)

f(t)=20\left(\frac{1}{2}\right)^{\frac{t}{4}}

\newline

(C)

f(t)=20\left(\frac{1}{2}\right)^{3 t}

\newline

(D)

f(t)=20\left(\frac{1}{2}\right)^{4 t}

Understand the problem: Understand the problem. $\newline$ We need to express the function $f(t) = 20\left(\frac{1}{8}\right)^t$ with a base of $\frac{1}{2}$ instead of $\frac{1}{8}$ .
Express as power of: Express $(1)/(8)$ as a power of $(1)/(2)$ . Since $(1)/(8)$ is equal to $(1)/(2)^3$ , we can rewrite the function using this relationship.
Substitute in the function: Substitute $\frac{1}{8}$ with $\frac{1}{2}^3$ in the function. $\newline$ $f(t) = 20\left(\frac{1}{2}^3\right)^t$
Apply power rule: Apply the power of a power rule. $\newline$ When you raise a power to a power, you multiply the exponents. So, $(\frac{1}{2}^3)^t$ becomes $\frac{1}{2}^{3t}$ . $\newline$ f(t) = $20$ \left(\frac{ $1$ }{ $2$ }^{ $3$ t}\right)
Compare with answer choices: Compare the resulting function with the answer choices. The function we have now, $f(t) = 20\left(\frac{1}{2}\right)^{3t}$ , matches one of the given answer choices.