A function f(t) increases by 9 over every unit interval in t and f(0) = 0. Which could be a function rule for f(t)? Choices: (A)f(t) = -9t (B)f(t) = 9^t (C)f(t) = 9t (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: (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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Algebra 1

Simplify exponential expressions using exponent rules

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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.