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A function $f(t)$ increases by $9$ over every unit interval in $t$ and $f(0) = 0$ . $\newline$ Which could be a function rule for $f(t)$ ? $\newline$ Choices: $\newline$ (A) $f(t) = -9t$ $\newline$ (B) $f(t) = 9^t$ $\newline$ (C) $f(t) = 9t$ $\newline$ (D) $f(t)$ = $-t$ + $9$

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Simplify exponential expressions using exponent rules

Full solution

Q. A function

f(t)

increases by

9

over every unit interval in

t

and

f(0) = 0

.

\newline

Which could be a function rule for

f(t)

?

\newline

Choices:

\newline

(A)

f(t) = -9t

\newline

(B)

f(t) = 9^t

\newline

(C)

f(t) = 9t

\newline

(D)

f(t)

=

-t

+

9

Start and Function Analysis: Since $f(0) = 0$ , we know the function starts at $0$ when $t$ is $0$ . Now, we need to find a function that increases by $9$ for each unit increase in $t$ .
Option Evaluation: Let's check each option: $\newline$ (A) $f(t) = -9t$ would decrease by $9$ for each unit increase in $t$ , not increase.
Option A: (B) $f(t) = 9^t$ would increase exponentially, not by a constant rate of $9$ .
Option B: $C$ $f(t) = 9t$ would increase by $9$ for each unit increase in $t$ , which matches what we're looking for.
Option C: $D$ $f(t) = -t + 9$ would decrease by $1$ for each unit increase in $t$ and start at $9$ when $t$ is $0$ , which doesn't fit the description.

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