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Write an exponential function in the form
y=ab^(x) that goes through the points
(0,9) and
(2,324).
Answer:

Write an exponential function in the form $y=a b^{x}$ that goes through the points $(0,9)$ and $(2,324)$ . $\newline$ 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

(2,324)

.

\newline

Answer:

Find 'a' value: Use the first point $(0,9)$ to find the value of 'a'. $\newline$ The general form of an exponential function is $y = ab^x$ . When $x = 0$ , the equation simplifies to $y = a$ , because $b^0 = 1$ for any non-zero value of $b$ . $\newline$ Substitute $x = 0$ and $y = 9$ into the equation to find 'a'. $\newline$ $9 = a \cdot b^0$ $\newline$ $9 = a \cdot 1$ $\newline$ $y = ab^x$ $0$
Find 'b' value: Use the second point $(2,324)$ to find the value of 'b'. $\newline$ Now that we know $a$ is $9$ , we can substitute $a$ and the coordinates of the second point into the equation to solve for 'b'. $\newline$ $324 = 9 \times b^2$ $\newline$ To find $b$ , divide both sides by $9$ . $\newline$ $\frac{324}{9} = b^2$ $\newline$ $36 = b^2$ $\newline$ To find the value of 'b', take the square root of both sides. $\newline$ $b = \sqrt{36}$ $\newline$ $a$ $0$
Write final exponential function: Write the final exponential function using the values of 'a' and 'b'. $\newline$ Now that we have $a = 9$ and $b = 6$ , we can write the exponential function as: $\newline$ $y = 9 \times 6^x$

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