Respuesta :
Given:
An exponential equation passes through the points (0,4) and (2,9).
To find:
Exponential equation that passes through the given points.
Solution:
Let the required exponential function is:
[tex]y=ab^x[/tex] ...(i)
The function passes through the points (0,4) and (2,9). It means the above equation must be true for these points.
[tex]4=ab^0[/tex]
[tex]4=a(1)[/tex]
[tex]4=a[/tex]
And,
[tex]9=ab^2[/tex]
Substituting [tex]a=4[/tex], we get
[tex]9=(4)b^2[/tex]
[tex]\dfrac{9}{4}=b^2[/tex]
[tex]\pm \sqrt{\dfrac{9}{4}}=b[/tex]
[tex]\pm \dfrac{3}{2}=b[/tex]
In an exponential function b>0. So, [tex]b=\dfrac{3}{2}[/tex].
Putting [tex]a=4,b=\dfrac{3}{2}[/tex] in (i), we get
[tex]y=4\left(\dfrac{3}{2}\right)^x[/tex]
Therefore, the required exponential function is [tex]y=4\left(\dfrac{3}{2}\right)^x[/tex].
