Answer:
The exponential function that goes through [tex](x_{1},y_{1}) = (0,20)[/tex] and [tex](x_{2}, y_{2}) = (2,720)[/tex] is [tex]y = 20\cdot 6^{x}[/tex].
Step-by-step explanation:
Let be an exponential function of the form [tex]y = a\cdot b^{x}[/tex] that goes through [tex](x_{1},y_{1}) = (0,20)[/tex] and [tex](x_{2}, y_{2}) = (2,720)[/tex]. Then, we have the following system of equations:
[tex]20 = a\cdot b^{0}[/tex] (1)
[tex]720 = a\cdot b^{2}[/tex] (2)
By dividing (2) by (1), we obtain the value for [tex]b[/tex]:
[tex]\frac{720}{20} = b^{2}[/tex]
[tex]b = \sqrt{\frac{720}{20} }[/tex]
[tex]b = 6[/tex]
And the value for [tex]a[/tex] is found by (1):
[tex]a = 20[/tex]
The exponential function that goes through [tex](x_{1},y_{1}) = (0,20)[/tex] and [tex](x_{2}, y_{2}) = (2,720)[/tex] is [tex]y = 20\cdot 6^{x}[/tex].
