QuestionApril 20, 2026

7) (10 points) Write an exponential function for a graph that passes through the points (1,12) and (2,48)

7) (10 points) Write an exponential function for a graph that passes through the points (1,12) and (2,48)
7) (10 points) Write an exponential function for a graph that passes through the points (1,12) and (2,48)

Solution
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Answer

f(x) = 3 \cdot 4^x Explanation 1. Assume general exponential form Let f(x) = a \cdot b^x where a and b are constants. 2. Use the first point (1, 12) 12 = a \cdot b^1 \Rightarrow a \cdot b = 12 3. Use the second point (2, 48) 48 = a \cdot b^2 4. Solve for b Divide the second equation by the first: \frac{48}{12} = \frac{a \cdot b^2}{a \cdot b} \Rightarrow 4 = b \Rightarrow b = 4 5. Solve for a From a \cdot b = 12: a \cdot 4 = 12 \Rightarrow a = 3 6. Write final function f(x) = 3 \cdot 4^x

Explanation

1. Assume general exponential form <br /> Let $f(x) = a \cdot b^x$ where $a$ and $b$ are constants. <br /><br />2. Use the first point $(1, 12)$ <br /> $12 = a \cdot b^1 \Rightarrow a \cdot b = 12$ <br /><br />3. Use the second point $(2, 48)$ <br /> $48 = a \cdot b^2$ <br /><br />4. Solve for $b$ <br /> Divide the second equation by the first: <br />$\frac{48}{12} = \frac{a \cdot b^2}{a \cdot b} \Rightarrow 4 = b \Rightarrow b = 4$ <br /><br />5. Solve for $a$ <br /> From $a \cdot b = 12$: <br />$a \cdot 4 = 12 \Rightarrow a = 3$ <br /><br />6. Write final function <br /> $f(x) = 3 \cdot 4^x$
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