How does g(x) = 10^x change over the interval from x = 1 to x = 3? Choices: [[g(x) increases by a factor of 20][g(x) increases by a factor of 100][g(x) decreases by 20%][g(x) decreases by a factor of 10]]

Evaluate g(x) at lower bound: Evaluate g(x) at the lower bound of the interval. We need to find the value of g(x) when x = 1. Calculate g(1) = 10^1.Evaluate g(x) at upper bound: Evaluate g(x) at the upper bound of the interval. We need to find the value of g(x) when x = 3. Calculate g(3) = 10^3.Determine direction of change: Determine the direction of change in g(x) over the interval. Compare g(1) and g(3) to see if g(x) increases or decreases. Since 10^3 is greater than 10^1, g(x) increases from x = 1 to x = 3.Calculate growth factor: Calculate the factor by which g(x) increases over the interval. Divide g(3) by g(1) to find the growth factor. Calculate the growth factor as 10^3 / 10^1 = 10^(3-1) = 10^2 = 100.Match growth factor with choices: Match the calculated growth factor with the given choices. The growth factor is 100, so g(x) increases by a factor of 100 from x = 1 to x = 3.

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How does $g(x) = 10^x$ change over the interval from $x = 1$ to $x = 3$ ? $\newline$ Choices: $\newline$ $g(x)$ increases by a factor of $20$ $\newline$ $g(x)$ 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 2

Describe linear and exponential growth and decay

Full solution

Q. How does

g(x) = 10^x

change over the interval from

x = 1

x = 3

\newline

Choices:

\newline

g(x)

increases by a factor of

20

\newline

g(x)

increases by a factor of

100

\newline

g(x)

decreases by

20\%

\newline

g(x)

decreases by a factor of

10

Evaluate $g(x)$ at lower bound: Evaluate $g(x)$ at the lower bound of the interval. $\newline$ We need to find the value of $g(x)$ when $x = 1$ . $\newline$ Calculate $g(1) = 10^1$ .
Evaluate $g(x)$ at upper bound: Evaluate $g(x)$ at the upper bound of the interval. $\newline$ We need to find the value of $g(x)$ when $x = 3$ . $\newline$ Calculate $g(3) = 10^3$ .
Determine direction of change: Determine the direction of change in $g(x)$ over the interval. $\newline$ Compare $g(1)$ and $g(3)$ to see if $g(x)$ increases or decreases. $\newline$ Since $10^3$ is greater than $10^1$ , $g(x)$ increases from $x = 1$ to $x = 3$ .
Calculate growth factor: Calculate the factor by which $g(x)$ increases over the interval. $\newline$ Divide $g(3)$ by $g(1)$ to find the growth factor. $\newline$ Calculate the growth factor as: $\newline$ $\frac{10^3}{10^1} = 10^{3-1} = 10^2 = 100$
Match growth factor with choices: Match the calculated growth factor with the given choices. $\newline$ The growth factor is $100$ , so $g(x)$ increases by a factor of $100$ from $x = 1$ to $x = 3$ .