How does g(x) = 10^x change over the interval from x = 3 to x = 4? Choices: [[g(x) increases by a factor of 10][g(x) increases by a factor of 100][g(x) decreases by 20%][g(x) decreases by a factor of 10]]

Given function: We have: g(x) = 10^x Find the value of g(3). Substitute x = 3 in g(x) = 10^x. g(3) = 10^3 g(3) = 1000Find g(3): We have: g(x) = 10^x Find the value of g(4). Substitute x = 4 in g(x) = 10^x. g(4) = 10^4 g(4) = 10000Find g(4): We found: g(3) = 1000 g(4) = 10000 Divide g(4) by g(3). g(4) / g(3) = 10000 / 1000 = 10Calculate ratio: Change: g(4) / g(3) = 10 Is g(x) increasing or decreasing? The value of g(x) increases from 1000 to 10000. So, g(x) increases.Behavior of g(x): We found: Change: factor of 10 Behavior of g(x): increases How does g(x) = 10^x change from x = 3 to x = 4? We found that g(x) increases and the factor is 10. g(x) increases by a factor of 10.

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How does $g(x) = 10^x$ change over the interval from $x = 3$ to $x = 4$ ? $\newline$ Choices: $\newline$ $g(x)$ increases by a factor of $10$ $\newline$ $g(x)$ increases by a factor of $100$ $\newline$ $g(x)$ decreases by $20\%$ $\newline$ $g(x)$ decreases by a factor of $10$

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Math Problems

Algebra 1

Linear functions over unit intervals

Full solution

Q. How does

g(x) = 10^x

change over the interval from

x = 3

x = 4

\newline

Choices:

\newline

g(x)

increases by a factor of

10

\newline

g(x)

increases by a factor of

100

\newline

g(x)

decreases by

20\%

\newline

g(x)

decreases by a factor of

10

Given function: We have: $g(x) = 10^x$ Find the value of $g(3)$ . Substitute $x = 3$ in $g(x) = 10^x$ . $g(3) = 10^3$ $g(3) = 1000$
Find $g(3)$ : We have: $g(x) = 10^x$ Find the value of $g(4)$ . Substitute $x = 4$ in $g(x) = 10^x$ . $g(4) = 10^4$ $g(4) = 10000$
Find $g(4)$ : We found: $g(3) = 1000$ $g(4) = 10000$ Divide $g(4)$ by $g(3)$ . $\frac{g(4)}{g(3)} = \frac{10000}{1000} = 10$
Calculate ratio: Change: $g(4) / g(3) = 10$
Is $g(x)$ increasing or decreasing?
The value of $g(x)$ increases from $1000$ to $10000$ .
So, $g(x)$ increases.
Behavior of $g(x)$ : We found: Change: factor of $10$ Behavior of $g(x)$ : increases How does $g(x) = 10^x$ change from $x = 3$ to $x = 4$ ? We found that $g(x)$ increases and the factor is $10$ . $g(x)$ increases by a factor of $10$ .