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Chapter 10: Q34. (page 528)

Write an exponential function whose graph passes through the points $(0, 3) and (1, 15)$ .

Short Answer

Expert verified

The exponential function passing through the given points is $y = 3 {(5)}^{x}$ .

Step by step solution

01

Step 1. Write down the given information.

The given points are $(0, 3) and (1, 15)$ .

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 $(0, 3) and (1, 15)$ in exponential function $y = a b^{x}$ .

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

Similarly,

$\begin{array}{l} y = a b^{x} \\ (15) = a b^{(1)} .... (Forthepoint (1, 15)) \\ 15 = (3) b .... (\begin{array}{l} From (2) \\ a = 3 \end{array}) \\ b = 5.... (鈭� b > 0) \end{array}$

Plugging $a = 3, b = 5$ in (1) gives $y = 3 {(5)}^{x}$ which is the required exponential function passing through the given points.

04

Step 4. Conclusion.

The exponential function passing through the given points is $y = 3 {(5)}^{x}$ .

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Most popular questions from this chapter

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