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Find the equation of the exponential given
(0,1) and
(-1,3)

$1$ . Find the equation of the exponential given $(0,1)$ and $(-1,3)$

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Full solution

Q.

1

. Find the equation of the exponential given

(0,1)

and

(-1,3)

Identify General Form: Identify the general form of an exponential function. $\newline$ General form: $y = ab^x$
Find 'a' Using Point: Use the point $(0,1)$ to find 'a'. $\newline$ Substitute $x = 0$ and $y = 1$ into the equation: $\newline$ $1 = a b^0$ $\newline$ Since $b^0 = 1$ for any $b \neq 0$ , $\newline$ $1 = a \cdot 1$ $\newline$ $a = 1$
Substitute 'a' and Use Point: Substitute 'a' back into the equation and use the point $(-1,3)$ . $\newline$ With $a = 1$ , the equation simplifies to $y = b^x$ . $\newline$ Substitute $x = -1$ and $y = 3$ : $\newline$ $3 = b^{-1}$ $\newline$ $b^{-1} = 3$ $\newline$ $b = \frac{1}{3}$

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