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Find the formula for an exponential function that passes through the two points given. (x, y) = (-1, 9/2) and (x, y) = (3, 72)

f(x)=​

User Ronni
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1 Answer

4 votes

Answer:


f(x)=9\cdot 2^x

Explanation:

The general form of an exponential function is:


\Large\boxed{y=ab^x}

where:

  • a is the initial value (y-intercept).
  • b is the base (growth/decay factor) in decimal form.

To find the formula for an exponential function that passes through points (-1, 9/2) and (3, 72), substitute both points into the formula to create two equations in terms of a and b:


\textsf{Equation\;1:} \quad ab^(-1)=(9)/(2)


\textsf{Equation\;2:} \quad ab^(3)=72

Divide equation 2 by equation 1 to eliminate a, then solve for b:


(ab^3)/(ab^(-1))=(72)/((9)/(2))


(b^3)/(b^(-1))=(72 \cdot 2)/(9)


b^(3-(-1))=(144)/(9)


b^4=16


b=\sqrt[4]{16}


b=2

Therefore, the value of b is 2.

Substitute the found value of b into the second equation, and solve for a:


\begin{aligned}ab^3&=72\\b=2 \implies a(2)^3&=72\\8a&=72\\a&=9\end{aligned}

Therefore, the value of a is 9.

Therefore, the formula for an exponential function that passes through points (-1, 9/2) and (3, 72) is:


\large\boxed{f(x)=9\cdot 2^x}

Find the formula for an exponential function that passes through the two points given-example-1
User Aycanadal
by
8.2k points

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