How does f(t)=8^t change over the interval from t=4 to t=6? Choices: [[f(t) decreases by a factor of 16][f(t) increases by 16%][f(t) decreases by factor of 8[[f(t) increases by a factor of 64]]

Given function: We have: f(t) = 8^t Find the value of f(4). Substitute t = 4 in f(t) = 8^t. f(4) = 8^4 f(4) = 4096Find f(4): We have: f(t) = 8^t Find the value of f(6). Substitute t = 6 in f(t) = 8^t. f(6) = 8^6 f(6) = 262144Find f(6): We found: f(4) = 4096 f(6) = 262144 Divide f(6) by f(4) to find the factor of change. f(6) / f(4) = 262144 / 4096 = 64Calculate factor of change: Change: f(6) / f(4) = 64 Is f(t) increasing or decreasing? The value of f(t) increases from 4096 to 262144. So, f(t) increases.Behavior of f(t): We found: Change: factor of 64 Behavior of f(t): increases How does f(t) = 8^t change from t = 4 to t = 6? We found that f(t) increases and the factor is 64. f(t) increases by a factor of 64.

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How does $f(t)=8^t$ change over the interval from $t=4$ to $t=6$ ? $\newline$ Choices: $\newline$ $\text{f(t) decreases by a factor of 16}$ $\newline$ $\text{f(t) increases by 16\%}$ $\newline$ $\text{f(t) decreases by factor of 8}$ $\newline$ $\text{f(t) increases by a factor of 64}$

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Math Problems

Algebra 1

Linear functions over unit intervals

Full solution

Q. How does

f(t)=8^t

change over the interval from

t=4

t=6

\newline

Choices:

\newline

\text{f(t) decreases by a factor of 16}

\newline

\text{f(t) increases by 16\%}

\newline

\text{f(t) decreases by factor of 8}

\newline

\text{f(t) increases by a factor of 64}

Given function: We have:
$f(t) = 8^t$
Find the value of $f(4)$ .
Substitute $t = 4$ in $f(t) = 8^t$ .
$f(4) = 8^4$
$f(4) = 4096$
Find $f(4)$ : We have: $f(t) = 8^t$ Find the value of $f(6)$ . Substitute $t = 6$ in $f(t) = 8^t$ . $f(6) = 8^6$ $f(6) = 262144$
Find $f(6)$ : We found: $f(4) = 4096$ $f(6) = 262144$ Divide $f(6)$ by $f(4)$ to find the factor of change. $f(6) / f(4) = 262144 / 4096 = 64$
Calculate factor of change: Change: $\frac{f(6)}{f(4)} = 64$ Is $f(t)$ increasing or decreasing? The value of $f(t)$ increases from $4096$ to $262144$ . So, $f(t)$ increases.
Behavior of $f(t)$ : We found: Change: factor of $64$ Behavior of $f(t)$ : increases How does $f(t) = 8^t$ change from $t = 4$ to $t = 6$ ? We found that $f(t)$ increases and the factor is $64$ . $f(t)$ increases by a factor of $64$ .