Answer:
[tex]y = 3 \times 4^{x}[/tex]
Step-by-step explanation:
The general form of an exponential function is [tex]y = a\times b^{x}[/tex] .......... (1) where a ≠ 0 and b > 0 and b ≠ 1.
Now, the two points [tex](-2,\frac{3}{16})[/tex] and (2,48) satisfies the equation (1).
So, [tex]\frac{3}{16} = a \times b^{- 2}[/tex] ........... (2)
And, [tex]48 = a\times b^{2}[/tex] .......... (3)
Now, dividing equation (3) by equation (2), we get
[tex]\frac{48 \times 16}{3} = b^{4}[/tex]
⇒ b = 4
Again, from equation (3) we get,
[tex]48 = a\times 4^{2}[/tex]
⇒ a = 3
Therefore, the exponential function is [tex]y = 3 \times 4^{x}[/tex]. (Answer)
