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Write an exponential function in the form
y=ab^(x) that goes through the points
(0,3) and
(4,1875).
Answer:

Write an exponential function in the form $y=a b^{x}$ that goes through the points $(0,3)$ and $(4,1875)$ . $\newline$ 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

(0,3)

and

(4,1875)

.

\newline

Answer:

Find 'a' value: Use the first point $(0,3)$ 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 any nonzero number raised to the power of $0$ is $1$ . Therefore, we can substitute the given point $(0,3)$ into the equation to find 'a'. $\newline$ $y = ab^0$ $\newline$ $3 = a \times 1$ $\newline$ $a = 3$
Find 'b' value: Use the second point $(4,1875)$ to find the value of 'b'. $\newline$ Now that we know 'a' is $3$ , we can substitute the second point $(4,1875)$ into the equation $y = ab^x$ and solve for 'b'. $\newline$ $1875 = 3b^4$ $\newline$ To isolate $b^4$ , divide both sides by $3$ . $\newline$ $b^4 = \frac{1875}{3}$ $\newline$ $b^4 = 625$ $\newline$ To find 'b', take the fourth root of both sides. $\newline$ $b = 625^{\frac{1}{4}}$ $\newline$ $3$ $0$
Write final exponential function: Write the final exponential function. $\newline$ Now that we have both 'a' and 'b', we can write the exponential function. $\newline$ $a = 3$ $\newline$ $b = 5$ $\newline$ The exponential function is $y = ab^x$ . $\newline$ Substitute 'a' and 'b' into the equation. $\newline$ $y = 3 \times 5^x$

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