A function h(t) increases by 2 over every unit interval in t and h(0) = 0. Which could be a function rule for h(t)? Choices: (A)h(t) = 2^t (B)h(t) = -t + 2 (C)h(t) = 2t (D)h(t) = -t/2

Check Initial Condition: Check the initial condition h(0) = 0 for each function choice. (A) h(0) = 2^0 = 1, not 0. (B) h(0) = -0 + 2 = 2, not 0. (C) h(0) = 2*0 = 0, this one works. (D) h(0) = -0/2 = 0, this one also works.Check Rate of Increase: Check the rate of increase for each function that passed Step 1. (C) h(1) = 2*1 = 2, so it increases by 2 over one unit interval. (D) h(1) = -1/2, it decreases, not increases.Choose Correct Function: Choose the correct function based on the initial condition and rate of increase. The correct function is (C) h(t) = 2t because it satisfies both the initial condition and the rate of increase.

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Q. A function

h(t)

increases by

2

over every unit interval in

t

and

h(0) = 0

\newline

Which could be a function rule for

h(t)

\newline

Choices:

\newline

(A)

h(t) = 2^t

\newline

(B)

h(t) = -t + 2

\newline

(C)

h(t) = 2t

\newline

(D)

h(t) = \frac{-t}{2}

Check Initial Condition: Check the initial condition $h(0) = 0$ for each function choice. $\newline$ (A) $h(0) = 2^0 = 1$ , not $0$ . $\newline$ (B) $h(0) = -0 + 2 = 2$ , not $0$ . $\newline$ (C) $h(0) = 2\times0 = 0$ , this one works. $\newline$ (D) $h(0) = -0/2 = 0$ , this one also works.
Check Rate of Increase: Check the rate of increase for each function that passed Step $1$ . $\newline$ (C) $h(1) = 2\times1 = 2$ , so it increases by $2$ over one unit interval. $\newline$ (D) $h(1) = -\frac{1}{2}$ , it decreases, not increases.
Choose Correct Function: Choose the correct function based on the initial condition and rate of increase. $\newline$ The correct function is (C) $h(t) = 2t$ because it satisfies both the initial condition and the rate of increase.