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The exponential function
h is graphed in the
xy-plane. If the graph contains the points
(0,18) and
(4,3), which of the following could be
h ?
Choose 1 answer:
(A)
h(x)=16((1)/(2))^(x)+2
(B)
h(x)=16((1)/(2))^(x)+3
(c)
h(x)=18((1)/(3))^((x)/(2))
(D)
h(x)=18((1)/(2))^(x)-2

The exponential function $h$ is graphed in the $x y$ -plane. If the graph contains the points $(0,18)$ and $(4,3)$ , which of the following could be $h$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $h(x)=16\left(\frac{1}{2}\right)^{x}+2$ $\newline$ (B) $h(x)=16\left(\frac{1}{2}\right)^{x}+3$ $\newline$ (C) $h(x)=18\left(\frac{1}{3}\right)^{\frac{x}{2}}$ $\newline$ (D) $h(x)=18\left(\frac{1}{2}\right)^{x}-2$

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Compare linear and exponential growth

Full solution

Q. The exponential function

h

is graphed in the

x y

-plane. If the graph contains the points

(0,18)

and

(4,3)

, which of the following could be

h

?

\newline

Choose

1

answer:

\newline

(A)

h(x)=16\left(\frac{1}{2}\right)^{x}+2

\newline

(B)

h(x)=16\left(\frac{1}{2}\right)^{x}+3

\newline

(C)

h(x)=18\left(\frac{1}{3}\right)^{\frac{x}{2}}

\newline

(D)

h(x)=18\left(\frac{1}{2}\right)^{x}-2

Test option (A) with $(0,18)$ : We will test each function option by plugging in the given points to see if they satisfy the function. $\newline$ First, let's test option (A) with the point $(0,18)$ . $\newline$ $h(x) = 16(\frac{1}{2})^x + 2$ $\newline$ $h(0) = 16(\frac{1}{2})^0 + 2$ $\newline$ $h(0) = 16(1) + 2$ $\newline$ $h(0) = 16 + 2$ $\newline$ $h(0) = 18$
Test option (A) with $(4,3)$ : Now let's test option (A) with the point $(4,3)$ . $h(4) = 16(\frac{1}{2})^4 + 2$ $h(4) = 16(\frac{1}{16}) + 2$ $h(4) = 1 + 2$ $h(4) = 3$
Option (A) satisfies both points: Since option (A) satisfies both points $(0,18)$ and $(4,3)$ , we have found a function that could represent $h$ . We do not need to test the other options because the question asks for ＂which of the following could be $h$ ＂ and not ＂which of the following are all possible $h$ ＂.

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