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Expert-verified Found in: Page 528 ### Algebra 2

Book edition Middle English Edition
Author(s) Carter
Pages 804 pages
ISBN 9780079039903 # Write an exponential function whose graph passes through the points $\left(0,7\right)\text{and}\left(2,63\right)$.

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

See the step by step solution

## Step 1. Write down the given information.

The given points are $\left(0,7\right)\text{and}\left(2,63\right)$.

## Step 2. Concept used.

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

## Step 3. Satisfying the given points in exponential function.

On satisfying the points $\left(0,7\right)\text{and}\left(2,63\right)$ in exponential function $y=a{b}^{x}$.

$\begin{array}{c}y=a{b}^{x}....\left(1\right)\\ \left(7\right)=a{b}^{\left(0\right)}....\left(\text{For the point}\left(0,7\right)\right)\\ a=7....\left(2\right)\end{array}$

Similarly,

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

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

## Step 4. Conclusion.

The exponential function passing through the given points is $y=7{\left(3\right)}^{x}$. ### Want to see more solutions like these? 