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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

01

Step 1. Write down the given information.

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

02

Step 2. Concept used.

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

03

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,

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

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 $(0, 3) and (- 1, 6)$ .

04

Step 4. Conclusion.

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

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