Log In Start studying!

Select your language

Suggested languages for you:

Americas

English (US)

Europe

Q35.

Expert-verified

Algebra 2

Found in: Page 528

Book edition Middle English Edition

Author(s) Carter

Pages 804 pages

ISBN 9780079039903

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later

Short Answer

Write an exponential function whose graph passes through the points $(0, 7) and (2, 63)$ .

The exponential function passing through the given points is $y = 7 {(3)}^{x}$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Write down the given information.

The given points are $(0, 7) and (2, 63)$ .

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 $(0, 7) and (2, 63)$ in exponential function $y = a b^{x}$ .

$\begin{matrix} y = a b^{x} .... (1) \\ (7) = a b^{(0)} .... (For the point (0, 7)) \\ a = 7.... (2) \end{matrix}$

Similarly,

$\begin{matrix} y = a b^{x} \\ (63) = a b^{(2)} .... (For the point (2, 63)) \\ (63) = (7) b^{(2)} .... (\begin{array}{l} From (2) \\ a = 7 \end{array}) \\ b = 3.... (∵ b > 0) \end{matrix}$

Plugging $a = 7, b = 3$ in (1) gives $y = 7 {(3)}^{x}$ which is the required exponential function passing through the given points.

Step 4. Conclusion.

The exponential function passing through the given points is $y = 7 {(3)}^{x}$ .

Most popular questions for Math Textbooks

Solve the inequality $5^{2 x + 3} \leq 125$ . Check your solution.

Find the inverse of the matrix

[\begin{matrix} - 5 & 6 \\ - 11 & 3 \end{matrix}]

if it exists.

Solve the equation $2^{3 x + 5} = 128$ . Check your solution.

Solve the equation $9^{2 y - 1} = 27^{y}$ . Check your solution.

Give an example of a value of $b$ for which $y = b^{x}$ represents exponential decay.

Want to see more solutions like these?

Sign up for free to discover our expert answers

Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free