Chapter 10: Q11. (page 528)

Write an exponential function whose graph passes through the points $(0, 3) and (- 1, 6)$ .

Short Answer

Expert verified

The exponential function passing through the given points is $y = 3 {(\frac{1}{2})}^{x}$ .

Step by step solution

Step 1. Write down the given information.

The given points are $(0, 3) and (- 1, 6)$ .

Step 2. Concept used.

The exponential function is of the form $y = a b^{x}$ where $a \neq 0, b \neq 1 and b > 0$ .

Step 3. Satisfying the given points in exponential function.

On satisfying the points $(0, 3) and (- 1, 6)$ in exponential function $y = a b^{x}$ .

$\begin{matrix} y = a b^{x} .... (1) \\ (3) = a b^{(0)} .... (Forthepoint (0, 3)) \\ 3 = a \\ a = 3.... (2) \end{matrix}$

Similarly,

$\begin{matrix} y = a b^{x} \\ (6) = a b^{(- 1)} .... (Forthepoint (- 1, 6)) \\ 6 = \frac{a}{b} \\ b = \frac{a}{6} \\ b = \frac{(3)}{6} .... (\begin{array}{l} From (2) \\ a = 3 \end{array}) \\ b = \frac{1}{2} \end{matrix}$

Plugging $a = 3, b = \frac{1}{2}$ in (1) gives $y = 3 {(\frac{1}{2})}^{x}$ which is the required exponential function passing through the given points $(0, 3) and (- 1, 6)$ .

Step 4. Conclusion.

The exponential function passing through the given points is $y = 3 {(\frac{1}{2})}^{x}$

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Write an exponential function whose graph passes through the points $(0, 3) and (- 1, 6)$ .

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Satisfying the given points in exponential function.

Step 4. Conclusion.

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Write an exponential function whose graph passes through the points 0,3and-1,6.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Satisfying the given points in exponential function.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

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Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

Write an exponential function whose graph passes through the points $(0, 3) and (- 1, 6)$ .