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Write an exponential function in the form
y=ab^(x) that goes through the points
(0,14) and
(4,1134).
Answer:

Write an exponential function in the form $y=a b^{x}$ that goes through the points $(0,14)$ and $(4,1134)$ . $\newline$ Answer:

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Convert between exponential and logarithmic form

Full solution

Q. Write an exponential function in the form

y=a b^{x}

that goes through the points

(0,14)

and

(4,1134)

.

\newline

Answer:

Find a Value of a: We need to find the values of $a$ and $b$ for the exponential function $y=ab^{x}$ that passes through the points $(0,14)$ and $(4,1134)$ . Let's start by using the point $(0,14)$ . Substitute $x=0$ and $y=14$ into the equation $y=ab^{x}$ . $y = ab^{0}$ $b$ $0$ Since any number raised to the power of $b$ $1$ is $b$ $2$ , we have: $b$ $3$ $b$ $4$ So, we have found the value of $a$ .
Find a Value of b: Now let's use the point $(4,1134)$ to find the value of b. $\newline$ Substitute $x=4$ , $y=1134$ , and $a=14$ into the equation $y=ab^{x}$ . $\newline$ $1134 = 14 \times b^4$ $\newline$ To solve for b, divide both sides by $14$ . $\newline$ $\frac{1134}{14} = b^4$ $\newline$ $81 = b^4$ $\newline$ Now, take the fourth root of both sides to solve for b. $\newline$ $b = 81^{\frac{1}{4}}$ $\newline$ $x=4$ $0$ $\newline$ We have found the value of b.
Write Exponential Function: Now that we have both $a$ and $b$ , we can write the exponential function. $a=14$ and $b=3$ , so the function is: $y = 14 \times 3^{x}$ This is the exponential function that goes through the points $(0,14)$ and $(4,1134)$ .

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