How do you write an exponential function whose graph passes through (0,7) and (2,63)?

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Answer 1 · 2017-04-24T07:23:47

$y = 7 \times 3^{x}$ $y=7xx3^x$ or $y = 7 \times {(- 3)}^{x}$ $y=7xx(-3)^x$

An exponential function is of the type $y = a b^{x}$ $y=ab^x$

As it passes through $(0, 7)$ $(0,7)$ , we have

$7 = a \times b^{0}$ $7=axxb^0$ or $7 = a \times 1$ $7=axx1$ i.e. $a = 7$ $a=7$ and function is #y=7b^x

it also passes through $(2, 63)$ $(2,63)$ and hence

$63 = 7 \times b^{2}$ $63=7xxb^2$ or $7 b^{2} = 63$ $7b^2=63$ or $b^{2} = 9$ $b^2=9$

and hence $b = + 3$ $b=+3$ or $b = - 3$ $b=-3$

and equations are $y = 7 \times 3^{x}$ $y=7xx3^x$ or $y = 7 \times {(- 3)}^{x}$ $y=7xx(-3)^x$