How does f(x)=5^x change over the interval from x=1 to x=3? Choices: [[f(x) decreases by a factor of 10][f(x) increases by 10%][f(x) increases by a factor of 25][f(x) increases by a factor of 10]]

Given function: We have: f(x) = 5^x Find the value of f(1). Substitute x = 1 in f(x) = 5^x. f(1) = 5^1 = 5Find f(1): We have: f(x) = 5^x Find the value of f(3). Substitute x = 3 in f(x) = 5^x. f(3) = 5^3 = 125Find f(3): We found: f(1) = 5 f(3) = 125 Calculate the factor of increase. Factor = f(3) / f(1) = 125 / 5 = 25Calculate factor: Change: f(3) / f(1) = 25 Is f(x) increasing or decreasing? The value of f(x) increases from 5 to 125. So, f(x) increases.Behavior of f(x): We found: Change: factor of 25 Behavior of f(x): increases How does f(x) = 5^x change from x = 1 to x = 3? We found that f(x) increases and the factor is 25. f(x) increases by a factor of 25.

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How does $f(x)=5^x$ change over the interval from $x=1$ to $x=3$ ? $\newline$ Choices: $\newline$ $\text{f(x) decreases by a factor of 10}$ $\newline$ $\text{f(x) increases by 10\%}$ $\newline$ $\text{f(x) increases by a factor of 25}$ $\newline$ $\text{f(x) increases by a factor of 10}$

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Math Problems

Algebra 1

Linear functions over unit intervals

Full solution

Q. How does

f(x)=5^x

change over the interval from

x=1

x=3

\newline

Choices:

\newline

\text{f(x) decreases by a factor of 10}

\newline

\text{f(x) increases by 10\%}

\newline

\text{f(x) increases by a factor of 25}

\newline

\text{f(x) increases by a factor of 10}

Given function: We have: $f(x) = 5^x$ Find the value of $f(1)$ . Substitute $x = 1$ in $f(x) = 5^x$ . $f(1) = 5^1 = 5$
Find $f(1)$ : We have: $f(x) = 5^x$ Find the value of $f(3)$ . Substitute $x = 3$ in $f(x) = 5^x$ . $f(3) = 5^3 = 125$
Find $f(3)$ : We found: $f(1) = 5$ $f(3) = 125$ Calculate the factor of increase. Factor = $\frac{f(3)}{f(1)} = \frac{125}{5} = 25$
Calculate factor: Change: $f(3) / f(1) = 25$ Is $f(x)$ increasing or decreasing? The value of $f(x)$ increases from $5$ to $125$ . So, $f(x)$ increases.
Behavior of $f(x)$ : We found: Change: factor of $25$ Behavior of $f(x)$ : increases How does $f(x) = 5^x$ change from $x = 1$ to $x = 3$ ? We found that $f(x)$ increases and the factor is $25$ . $f(x)$ increases by a factor of $25$ .