How does g(t)=9^t change over the interval from t=1 to t=3? Choices: [[g(t) decreases by a factor of 81][g(t) increases by a factor of 81][g(t) increases by 18%][g(t) decreases by 9%]]

Find g(1): We have the function g(t) = 9^t. Find the value of g(1). Substitute t = 1 into g(t) = 9^t. g(1) = 9^1 g(1) = 9Find g(3): We have the function g(t) = 9^t. Find the value of g(3). Substitute t = 3 into g(t) = 9^t. g(3) = 9^3 g(3) = 729Calculate Factor Change: We found: g(1) = 9 g(3) = 729 Calculate the factor by which g(t) has changed from t = 1 to t = 3. Divide g(3) by g(1). Factor change = g(3) / g(1) = 729 / 9 Factor change = 81Determine Increase or Decrease: Determine if g(t) increases or decreases. Since 729 is greater than 9, g(t) increases from t = 1 to t = 3.Summary: We found: Factor change: 81 Behavior of g(t): increases How does g(t) = 9^t change from t = 1 to t = 3? We found that g(t) increases and the factor by which it increases is 81. g(t) increases by a factor of 81.

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How does $g(t)=9^t$ change over the interval from $t=1$ to $t=3$ ? $\newline$ Choices: $\newline$ $\left[\text{g(t) decreases by a factor of } 81\right]$ $\newline$ $\left[\text{g(t) increases by a factor of } 81\right]$ $\newline$ $\left[\text{g(t) increases by } 18\%\right]$ $\newline$ $\left[\text{g(t) decreases by } 9\%\right]$

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Math Problems

Algebra 1

Describe linear and exponential growth and decay

Full solution

Q. How does

g(t)=9^t

change over the interval from

t=1

t=3

\newline

Choices:

\newline

\left[\text{g(t) decreases by a factor of } 81\right]

\newline

\left[\text{g(t) increases by a factor of } 81\right]

\newline

\left[\text{g(t) increases by } 18\%\right]

\newline

\left[\text{g(t) decreases by } 9\%\right]

Find $g(1)$ : We have the function $g(t) = 9^t$ . Find the value of $g(1)$ . $\newline$ Substitute $t = 1$ into $g(t) = 9^t$ . $\newline$ $g(1) = 9^1$ $\newline$ $g(1) = 9$
Find $g(3)$ : We have the function $g(t) = 9^t$ . Find the value of $g(3)$ . $\newline$ Substitute $t = 3$ into $g(t) = 9^t$ . $\newline$ $g(3) = 9^3$ $\newline$ $g(3) = 729$
Calculate Factor Change: We found: $\newline$ $g(1) = 9$ $\newline$ $g(3) = 729$ $\newline$ Calculate the factor by which $g(t)$ has changed from $t = 1$ to $t = 3$ . $\newline$ Divide $g(3)$ by $g(1)$ . $\newline$ Factor change = $\frac{g(3)}{g(1)} = \frac{729}{9}$ $\newline$ Factor change = $81$
Determine Increase or Decrease: Determine if $g(t)$ increases or decreases. $\newline$ Since $729$ is greater than $9$ , $g(t)$ increases from $t = 1$ to $t = 3$ .
Summary: We found: $\newline$ Factor change: $81$ $\newline$ Behavior of $g(t)$ : increases $\newline$ How does $g(t) = 9^t$ change from $t = 1$ to $t = 3$ ? $\newline$ We found that $g(t)$ increases and the factor by which it increases is $81$ . $\newline$ $g(t)$ increases by a factor of $81$ .