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Q35.

Expert-verifiedFound in: Page 528

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 $y=7{\left(3\right)}^{x}$.

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

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

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

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

Similarly,

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

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.

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

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