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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 ?

$f(t)=80(4)^{t}$ $\newline$ Which of the following is an equivalent form of the function $f$ in which the base of the exponent is $2$ ?

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Simplify radical expressions with variables

Full solution

Q.

f(t)=80(4)^{t}

\newline

Which of the following is an equivalent form of the function

f

in which the base of the exponent is

2

?

Express as Power of $2$ : First, we need to express $4$ as a power of $2$ because $4$ is $2$ squared, or $2^2$ .
Substitute in $f(t)$ : Now, we substitute $4$ with $2^2$ in the function $f(t)$ . So, $f(t)$ becomes $80(2^2)^t$ .
Apply Power Rule: Next, we apply the power of a power rule which states $(a^b)^c = a^{(b*c)}$ . $\newline$ So, $(2^2)^t$ becomes $2^{(2t)}$ .
Rewrite with New Base: Now, we rewrite the function $f(t)$ with the new base of the exponent. $f(t) = 80 \times 2^{2t}.$

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