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A function $h(t)$ increases by a factor of $6$ over every unit interval in $t$ and $h(0) = 1$ . $\newline$ Which could be a function rule for $h(t)$ ? $\newline$ Choices: $\newline$ (A) $h(t) = 6^t$ $\newline$ (B) $h(t) = 0.94^t$ $\newline$ (C) $h(t) = \frac{1}{6^t}$ $\newline$ (D) $h(t) = 6t$

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Identify linear and exponential functions

Full solution

Q. A function

h(t)

increases by a factor of

6

over every unit interval in

t

and

h(0) = 1

.

\newline

Which could be a function rule for

h(t)

?

\newline

Choices:

\newline

(A)

h(t) = 6^t

\newline

(B)

h(t) = 0.94^t

\newline

(C)

h(t) = \frac{1}{6^t}

\newline

(D)

h(t) = 6t

Find Initial Value: $h(t) = a \times 6^t$ , where $a$ is the initial value. $\newline$ Since $h(0) = 1$ , let's find $a$ . $\newline$ $h(0) = a \times 6^0 = a \times 1 = 1$ , so $a = 1$ .
Calculate Final Expression: Now we know $a = 1$ , so $h(t) = 1 \times 6^t$ . $\newline$ $h(t) = 6^t$ .

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