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

Given Function: We have: h(t) = 9^t Find the value of h(1). Substitute t = 1 in h(t) = 9^t. h(1) = 9^1 = 9Find h(1): We have: h(t) = 9^t Find the value of h(3). Substitute t = 3 in h(t) = 9^t. h(3) = 9^3 = 729Find h(3): We found: h(1) = 9 h(3) = 729 Calculate the factor of increase. Factor = h(3) / h(1) = 729 / 9 = 81Calculate Factor: Change: h(3) / h(1) = 81 Is h(t) increases, decreases, or remains unchanged? The value of h(t) increases from 9 to 729. So, h(t) increases.Behavior of h(t): We found: Change: factor of 81 Behavior of h(t): increases How does h(t) = 9^t change from t = 1 to t = 3? We found that h(t) increases and the factor is 81. h(t) increases by a factor of 81.

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

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Math Problems

Algebra 1

Linear functions over unit intervals

Full solution

Q. How does

h(t) = 9^t

change over the interval from

t=1

t=3

\newline

Choices:

\newline

\text{h(t) increases by 9\%}

\newline

\text{h(t) increases by a factor of 81 }

\newline

\text{h(t) decreases by a factor of 9\%}

\newline

\text{h(t) decreases by a factor of 18}

Given Function: We have: $h(t) = 9^t$ Find the value of $h(1)$ . Substitute $t = 1$ in $h(t) = 9^t$ . $h(1) = 9^1 = 9$
Find $h(1)$ : We have: $h(t) = 9^t$ Find the value of $h(3)$ . Substitute $t = 3$ in $h(t) = 9^t$ . $h(3) = 9^3 = 729$
Find $h(3)$ : We found: $h(1) = 9$ $h(3) = 729$ Calculate the factor of increase. Factor = $\frac{h(3)}{h(1)} = \frac{729}{9} = 81$
Calculate Factor: Change: $h(3) / h(1) = 81$ Is $h(t)$ increases, decreases, or remains unchanged? The value of $h(t)$ increases from $9$ to $729$ . So, $h(t)$ increases.
Behavior of $h(t)$ : We found: Change: factor of $81$ Behavior of $h(t)$ : increases How does $h(t) = 9^t$ change from $t = 1$ to $t = 3$ ? We found that $h(t)$ increases and the factor is $81$ . $h(t)$ increases by a factor of $81$ .