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Write an exponential function in the form
y=ab^(x) that goes through the points
(0,9) and
(4,144).
Answer:

Write an exponential function in the form $y=a b^{x}$ that goes through the points $(0,9)$ and $(4,144)$ . $\newline$ Answer:

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Write a linear equation from two points

Full solution

Q. Write an exponential function in the form

y=a b^{x}

that goes through the points

(0,9)

and

(4,144)

.

\newline

Answer:

Find 'a' value: Use the first point $(0,9)$ to find the value of 'a'. $\newline$ Since the point $(0,9)$ is on the graph of the function, when we substitute $x=0$ , we should get $y=9$ . $\newline$ So, $y = ab^{0} = a \times 1 = a$ . $\newline$ Therefore, $a = 9$ .
Find 'b' value: Use the second point $(4,144)$ to find the value of 'b'. $\newline$ We know that $a=9$ from Step $1$ , so we can substitute $a$ and the coordinates of the second point into the equation $y=ab^{x}$ to find 'b'. $\newline$ Substituting $x=4$ and $y=144$ , we get $144 = 9b^{4}$ . $\newline$ To solve for $b$ , we divide both sides by $9$ to isolate $b^{4}$ . $\newline$ $a=9$ $0$ $\newline$ $a=9$ $1$ $\newline$ To find $b$ , we take the fourth root of both sides. $\newline$ $a=9$ $3$ $\newline$ $a=9$ $4$
Write final exponential function: Write the final exponential function using the values of 'a' and 'b'. $\newline$ We have found that $a=9$ and $b=2$ . Now we can write the exponential function as: $\newline$ $y = ab^{(x)}$ $\newline$ $y = 9 \times 2^{(x)}$ $\newline$ This is the exponential function that goes through the points $(0,9)$ and $(4,144)$ .

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