How does f(t)=7^t change over the interval from t=1 to t=3? Choices: [[f(t) decreases by a factor of 7][f(t) decreases by 7%][f(t) increases by factor of 7[[f(t) increases by a factor of 49]]

Given function: We have: f(t) = 7^t Find the value of f(1). Substitute t = 1 in f(t) = 7^t. f(1) = 7^1 = 7Find f(1): We have: f(t) = 7^t Find the value of f(3). Substitute t = 3 in f(t) = 7^t. f(3) = 7^3 = 343Find f(3): We found: f(1) = 7 f(3) = 343 Calculate the change. f(3) / f(1) = 343 / 7 = 49Calculate change: Change: f(3) / f(1) = 49 Is f(t) increasing or decreasing? The value of f(t) increases from 7 to 343. So, f(t) increases.Behavior of f(t): We found: Change: 49 Behavior of f(t): increases How does f(t) = 7^t change from t = 1 to t = 3? We found that f(t) increases and the factor is 49. f(t) increases by a factor of 49.

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How does $f(t)=7^t$ change over the interval from $t=1$ to $t=3$ ? $\newline$ Choices: $\newline$ $\text{f(t) decreases by a factor of 7}$ $\newline$ $\text{f(t) increases by factor of 7}$ $\newline$ $\text{f(t) decreases by 7\%}$ $\newline$ $\text{f(t) increases by a factor of 49}$

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Math Problems

Algebra 1

Linear functions over unit intervals

Full solution

Q. How does

f(t)=7^t

change over the interval from

t=1

t=3

\newline

Choices:

\newline

\text{f(t) decreases by a factor of 7}

\newline

\text{f(t) increases by factor of 7}

\newline

\text{f(t) decreases by 7\%}

\newline

\text{f(t) increases by a factor of 49}

Given function: We have: $f(t) = 7^t$ Find the value of $f(1)$ . Substitute $t = 1$ in $f(t) = 7^t$ . $f(1) = 7^1 = 7$
Find $f(1)$ : We have: $f(t) = 7^t$ Find the value of $f(3)$ . Substitute $t = 3$ in $f(t) = 7^t$ . $f(3) = 7^3 = 343$
Find $f(3)$ : We found: $f(1) = 7$ $f(3) = 343$ Calculate the change. $\frac{f(3)}{f(1)} = \frac{343}{7} = 49$
Calculate change: Change: $\frac{f(3)}{f(1)} = 49$ Is $f(t)$ increasing or decreasing? The value of $f(t)$ increases from $7$ to $343$ . So, $f(t)$ increases.
Behavior of $f(t)$ : We found: Change: $49$ Behavior of $f(t)$ : increases How does $f(t) = 7^t$ change from $t = 1$ to $t = 3$ ? We found that $f(t)$ increases and the factor is $49$ . $f(t)$ increases by a factor of $49$ .